Academic literature on the topic 'Glass transition, statistical mechanics, disorder system'

Spin-models in random fields (RFs) are good representations of many impure materials. Their macroscopic collective behaviour is dominated by the fluctuations in the random fields which accumulate on large scales even if the local field is arbitrarily small. This feature is shared by other weakly disordered models, like flux lines or domain walls in random media. We review some of the main theoretical attempts to describe such systems. A modification of Harris’ argument demonstrates that at the critical point the RF disorder is relevant and that (hyper)scaling must be changed. A domain argument invented by Imry and Ma shows that long-range order is not destroyed by weak RFs in more than d=2 dimensions. This result is supported both by a more refined treatment of the domain argument and by considering the roughness of an isolated domain wall due to the randomness. The wall (or flux line) becomes rough due to disorder but if d>2 the wall remains a well-defined object in RF systems. Different approaches are used to calculate the roughness exponent ζ for walls and lines. Some applications of ζ for the description of type-II superconductors and incommensurate systems are given. More detailed calculations are possible for one-dimensional, Bethe-lattice or the hierarchical Dyson model systems, which confirm as a rule the more approximate treatment of the other sections. In one dimension there is an interesting relation between the statistical mechanics of these models and nonlinear dynamics. Non-classical critical behaviour occurs in RF systems for d<6 and is determined in general by three independent exponents which fulfil certain inequalities. The new exponent θ≡yJ>0 is related to the violation of conventional hyperscaling and is determined by the energy ~H0ξ0 of a correlated region of size ξ. In a renormalization group treatment, the temperature T turns out to be a (dangerous) irrelevant variable which is the most prominent property of the systems considered in this review. The irrelevance of thermal fluctuations on large scales produces metastability and hysteresis effects both in the transition region and in the ordered phase, only briefly considered here. These features occur also in other systems with a disordered T=0 fixed point like in the ordered phase of a spin-glass.

In this paper, we study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration p of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang–Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of p. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely p ~ 0.01, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small p (≃5%). With increasing p, the system changes into a spin glass and then to a ferromagnetic phase when p > 0.65. The phase diagram in the space (Tc, p) shows an asymmetry, unlike the case of the ±J Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor b is equal to ≃1/3 at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models.

A model binary alloy Ax B1−x where A and B represent ferromagnetic and paramagnetic transition metal respectively is considered within the framework of periodic Anderson model, and the effects of d-level disorder and variation of electron concentration due to alloying on the magnetic properties are investigated. The phase boundary, thermal behavior of magnetization and susceptibility of the alloy are obtained using HF approximation for the Coulomb interaction and the virtual crystal approximation for d-level disorder. The ferromagnetic state of alloy vanishes at a critical concentration xc which depends on d-band width, strength of s-d hybridization and the Coulomb interaction. The re-entrant magnetic phase is found within a small region of x for alloy with narrow d-band. For x≲xc, the magnetic properties resemble that of spin-glass system. For x≪xc, the alloy behaves like a Pauli paramagnet. The re-entrant and spin-glass-like phases are associated with the increase in d-level population as temperature decreases. Local moment for x≃1 decreases with temperature up to Tc whereas the reverse is the situation for alloy exhibiting spin-glass-like behavior.

The time correlation functions associated with the Onsager phenomenological coefficients for isothermal matter transport have been calculated by Monte Carlo simulation for a binary system (A,B) at the equiatomic composition according to the Kikuchi-Sato model of an order-disorder alloy with vacancy transport mechanism. The diagonal (AA) time correlation functions are positive, decay monotonically to zero, and exhibit a long time tail where they vary as t-n where t is time; the exponent n varies weakly with temperature at high temperatures and more rapidly as the temperature is lowered through the order-disorder transition temperature. In the region of short-range order the off-diagonal (AB) time correlation function is negative but otherwise shows similar behaviour to the diagonal one, although as the transition temperature is approached n varies more rapidly. At the transition temperature and below, the off-diagonal time correlation function increases from an initial negative value to a maximum where it is positive and then, at later times, decreases to zero. The implications of these observations for approximate theoretical calculations of the phenomenological coefficients are briefly indicated.Key words: diffusion, non-equilibrium phenomena, statistical mechanics, transport properties.

Silane-coated glass microspheres randomly embedded in an epoxy polymer matrix have been employed as a model system to investigate the degradation of disordered composite materials by water, and to test various models of deformation and fracture. Numerous composites containing sodalime (A) glass in the range 0 to 25% by volume were tested dry and immersed in saturated NaCl at 40 °C for periods up to 70 days before testing. Enhanced osmotic water uptake due to percolating interface damage was observed for composites containing more than 15% glass. The electrical resistance of similar composites filled with conducting spheres confirmed the existence of a percolation transition, though with high resistance values implying no direct contact of the spheres. Tensile measurements conducted on dry material at a nominal strain rate of about 10−3 s−1 showed an increase in elastic modulus and a decrease in the fracture strength with increasing glass content. New detail was apparent in these curves and confirmed by statistical analyses. For wet specimens, in addition to a general embrittlement effect of water absorption, there was a distinct plateau or small peak in fracture strength in the range 9 to 12% glass, and an abrupt drop between 12 and 15%. The plateau can be related to favorable crack interaction effects between disconnected clusters of interfaces just below the percolation threshold. The steep increase in elastic modulus with glass content seen in the dry material vanished entirely in wet material, which behaved like a porous polymer above 6% glass, owing to osmotic interface damage within particle clusters.

A glassy phase in disordered two dimensional (2D) electron systems may exist at low temperatures for electron densities lying intermediate between the Fermi liquid and Wigner crystal limits. The glassy phase is generated by the combined effects of disorder and the strong electron-electron correlations arising from the repulsive Coulomb interactions. Our approach here is motivated by the observation that at low electron densities the electron pair correlation function, as numerically determined for a non-disordered 2D system from Monte Carlo simulations, is very similar to the pair correlation function for a 2D classical system of hard discs. This suggests that theoretical approaches to 2D classical systems of hard discs may be of use in studying the disordered, low density electron problem. We use this picture to study its dynamics on the electron-liquid side of a glass transition. At long times the major relaxation process in the electron-liquid will be a rearrangement of increasingly large groups of the discs, rather than the movement of the discs separately. Such systems have been studied numerically and they display all the characteristics of glassy behaviour. There is a slowing down of the dynamics and a limiting value of the retarded spatial correlations. Motivated by the success of mode-coupling theories for hard spheres and discs in reproducing experimental results in classical fluids, we use the Mori formalism within a mode-coupling theory to obtain semi-quantitative insight into the role of electron correlations as they affect the time response of the weakly disordered 2D electron system at low densities.

A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated in a way that allows a description of the transition from the initial equilibrium state to the final metastable state without considering any kinetic processes. The RFOT and its applications for real molecular systems (multicomponent liquids with various intermolecular potentials, gel systems, etc.) are widely represented in English-language sources. However, these studies are practically not described in any Russian sources. This paper presents an overview of the studies carried out in this field. REFERENCES 1. Sanditov D. S., Ojovan M. I. Relaxation aspectsof the liquid—glass transition. Uspekhi FizicheskihNauk. 2019;189(2): 113–133. DOI: https://doi.org/10.3367/ufnr.2018.04.0383192. Tsydypov Sh. B., Parfenov A. N., Sanditov D. S.,Agrafonov Yu. V., Nesterov A. S. Application of themolecular dynamics method and the excited statemodel to the investigation of the glass transition inargon. Available at: http://www.isc.nw.ru/Rus/GPCJ/Content/2006/tsydypov_32_1.pdf (In Russ.). GlassPhysics and Chemistry. 2006;32(1): 83–88. DOI: https://doi.org/10.1134/S10876596060101113. Berthier L., Witten T. A. Glass transition of densefluids of hard and compressible spheres. PhysicalReview E. 2009;80(2): 021502. DOI: https://doi.org/10.1103/PhysRevE.80.0215024. Sarkisov G. N. Molecular distribution functionsof stable, metastable and amorphous classical models.Uspekhi Fizicheskih Nauk. 2002;172(6): 647–669. DOI:https://doi.org/10.3367/ufnr.0172.200206b.06475. Hoover W. G., Ross M., Johnson K. W., HendersonD., Barker J. A., Brown, B. C. Soft-sphere equationof state. The Journal of Chemical Physics, 1970;52(10):4931–4941. DOI: https://doi.org/10.1063/1.16727286. Cape J. N., Woodcock L. V. Glass transition in asoft-sphere model. The Journal of Chemical Physics,1980;72(2): 976–985. DOI: https://doi.org/10.1063/1.4392177. Franz S., Mezard M., Parisi G., Peliti L. Theresponse of glassy systems to random perturbations:A bridge between equilibrium and off-equilibrium.Journal of Statistical Physics. 1999;97(3–4): 459–488.DOI: https://doi.org/10.1023/A:10046029063328. Marc Mezard and Giorgio Parisi. Thermodynamicsof glasses: a first principles computation. J. of Phys.:Condens. Matter. 1999;11: A157–A165.9. Berthier L., Jacquin H., Zamponi F. Microscopictheory of the jamming transition of harmonic spheres.Physical Review E, 2011;84(5): 051103. DOI: https://doi.org/10.1103/PhysRevE.84.05110310. Berthier L., Biroli, G., Charbonneau P.,Corwin E. I., Franz S., Zamponi F. Gardner physics inamorphous solids and beyond. The Journal of ChemicalPhysics. 2019;151(1): 010901. DOI: https://doi.org/10.1063/1.5097175 11. Berthier L., Ozawa M., Scalliet C. Configurationalentropy of glass-forming liquids. The Journal ofChemical Physics. 2019;150(16): 160902. DOI: https://doi.org/10.1063/1.509196112. Bomont J. M., Pastore G. An alternative schemeto find glass state solutions using integral equationtheory for the pair structure. Molecular Physics.2015;113(17–18): 2770–2775. DOI: https://doi.org/10.1080/00268976.2015.103832513. Bomont J. M., Hansen J. P., Pastore G.Hypernetted-chain investigation of the random firstordertransition of a Lennard-Jones liquid to an idealglass. Physical Review E. 2015;92(4): 042316. DOI:https://doi.org/10.1103/PhysRevE.92.04231614. Bomont J. M., Pastore G., Hansen J. P.Coexistence of low and high overlap phases in asupercooled liquid: An integral equation investigation.The Journal of Chemical Physics. 2017;146(11): 114504.DOI: https://doi.org/10.1063/1.497849915. Bomont J. M., Hansen J. P., Pastore G. Revisitingthe replica theory of the liquid to ideal glass transition.The Journal of Chemical Physics. 2019;150(15): 154504.DOI: https://doi.org/10.1063/1.508881116. Cammarota C., Seoane B. First-principlescomputation of random-pinning glass transition, glasscooperative length scales, and numerical comparisons.Physical Review B. 2016;94(18): 180201. DOI: https://doi.org/10.1103/PhysRevB.94.18020117. Charbonneau P., Ikeda A., Parisi G., Zamponi F.Glass transition and random close packing above threedimensions. Physical Review Letters. 2011;107(18):185702. DOI: https://doi.org/10.1103/PhysRevLett.107.18570218. Ikeda A., Miyazaki K. Mode-coupling theory asa mean-field description of the glass transition.Physical Review Letters. 2010;104(25): 255704. DOI:https://doi.org/10.1103/PhysRevLett.104.25570419. McCowan D. Numerical study of long-timedynamics and ergodic-nonergodic transitions in densesimple fluids. Physical Review E. 2015;92(2): 022107.DOI: https://doi.org/10.1103/PhysRevE.92.02210720. Ohtsu H., Bennett T. D., Kojima T., Keen D. A.,Niwa Y., Kawano M. Amorphous–amorphous transitionin a porous coordination polymer. ChemicalCommunications. 2017;53(52): 7060–7063. DOI:https://doi.org/10.1039/C7CC03333H21. Schmid B., Schilling R. Glass transition of hardspheres in high dimensions. Physical Review E.2010;81(4): 041502. DOI: https://doi.org/10.1103/PhysRevE.81.04150222. Parisi G., Slanina, F. Toy model for the meanfieldtheory of hard-sphere liquids. Physical Review E.2000;62(5): 6554. DOI: https://doi.org/10.1103/Phys-RevE.62.655423. Parisi G., Zamponi F. The ideal glass transitionof hard spheres. The Journal of Chemical Physics.2005;123(14): 144501. DOI: https://doi.org/10.1063/1.204150724. Parisi G., Zamponi F. Amorphous packings ofhard spheres for large space dimension. Journal ofStatistical Mechanics: Theory and Experiment. 2006;03:P03017. DOI: https://doi.org/10.1088/1742-5468/2006/03/P0301725. Parisi G., Procaccia I., Shor C., Zylberg J. Effectiveforces in thermal amorphous solids with genericinteractions. Physical Review E. 2019;99(1): 011001. DOI:https://doi.org/10.1103/PhysRevE.99.01100126. Stevenson J. D., Wolynes P. G. Thermodynamic −kinetic correlations in supercooled liquids: a criticalsurvey of experimental data and predictions of therandom first-order transition theory of glasses. TheJournal of Physical Chemistry B. 2005;109(31): 15093–15097. DOI: https://doi.org/10.1021/jp052279h27. Xia X., Wolynes P. G. Fragilities of liquidspredicted from the random first order transition theoryof glasses. Proceedings of the National Academy ofSciences. 2000;97(7): 2990–2994. DOI: https://doi.org/10.1073/pnas.97.7.299028. Kobryn A. E., Gusarov S., Kovalenko A. A closurerelation to molecular theory of solvation formacromolecules. Journal of Physics: Condensed Matter.2016; 28 (40): 404003. DOI: https://doi.org/10.1088/0953-8984/28/40/40400329. Coluzzi B. , Parisi G. , Verrocchio P.Thermodynamical liquid-glass transition in a Lennard-Jones binary mixture. Physical Review Letters.2000;84(2): 306. DOI: https://doi.org/10.1103/PhysRevLett.84.30630. Sciortino F., Tartaglia P. Extension of thefluctuation-dissipation theorem to the physical agingof a model glass-forming liquid. Physical Review Letters.2001;86(1): 107. DOI: https://doi.org/10.1103/Phys-RevLett.86.10731. Sciortino, F. One liquid, two glasses. NatureMaterials. 2002;1(3): 145–146. DOI: https://doi.org/10.1038/nmat75232. Farr R. S., Groot R. D. Close packing density ofpolydisperse hard spheres. The Journal of ChemicalPhysics. 2009;131(24): 244104. DOI: https://doi.org/10.1063/1.327679933. Barrat J. L., Biben T., Bocquet, L. From Paris toLyon, and from simple to complex liquids: a view onJean-Pierre Hansen’s contribution. Molecular Physics.2015;113(17-18): 2378–2382. DOI: https://doi.org/10.1080/00268976.2015.103184334. Gaspard J. P. Structure of Melt and Liquid Alloys.In Handbook of Crystal Growth. Elsevier; 2015. 580 p.DOI: https://doi.org/10.1016/B978-0-444-56369-9.00009-535. Heyes D. M., Sigurgeirsson H. The Newtonianviscosity of concentrated stabilized dispersions:comparisons with the hard sphere fluid. Journal ofRheology. 2004;48(1): 223–248. DOI: https://doi.org/10.1122/1.163498636. Ninarello A., Berthier L., Coslovich D. Structureand dynamics of coupled viscous liquids. MolecularPhysics. 2015;113(17-18): 2707–2715. DOI: https://doi.org/10.1080/00268976.2015.103908937. Russel W. B., Wagner N. J., Mewis J. Divergencein the low shear viscosity for Brownian hard-spheredispersions: at random close packing or the glasstransition? Journal of Rheology. 2013;57(6): 1555–1567.DOI: https://doi.org/10.1122/1.482051538. Schaefer T. Fluid dynamics and viscosity instrongly correlated fluids. Annual Review of Nuclearand Particle Science. 2014;64: 125–148. DOI: https://doi.org/10.1146/annurev-nucl-102313-02543939. Matsuoka H. A macroscopic model thatconnects the molar excess entropy of a supercooledliquid near its glass transition temperature to itsviscosity. The Journal of Chemical Physics. 2012;137(20):204506. DOI: https://doi.org/10.1063/1.476734840. de Melo Marques F. A., Angelini R., Zaccarelli E.,Farago B., Ruta B., Ruocco, G., Ruzicka B. Structuraland microscopic relaxations in a colloidal glass. SoftMatter. 2015;11(3): 466–471. DOI: https://doi.org/10.1039/C4SM02010C41. Deutschländer S., Dillmann P., Maret G., KeimP. Kibble–Zurek mechanism in colloidal monolayers.Proceedings of the National Academy of Sciences.2015;112(22): 6925–6930. DOI: https://doi.org/10.1073/pnas.150076311242. Chang J., Lenhoff A. M., Sandler S. I.Determination of fluid–solid transitions in modelprotein solutions using the histogram reweightingmethod and expanded ensemble simulations. TheJournal of Chemical Physics. 2004;120(6): 3003–3014.DOI: https://doi.org/10.1063/1.163837743. Gurikov P., Smirnova I. Amorphization of drugsby adsorptive precipitation from supercriticalsolutions: a review. The Journal of Supercritical Fluids.2018;132: 105–125. DOI: https://doi.org/10.1016/j.supflu.2017.03.00544. Baghel S., Cathcart H., O’Reilly N. J. Polymericamorphoussolid dispersions: areviewofamorphization, crystallization, stabilization, solidstatecharacterization, and aqueous solubilization ofbiopharmaceutical classification system class II drugs.Journal of Pharmaceutical Sciences. 2016;105(9):2527–2544. DOI: https://doi.org/10.1016/j.xphs.2015.10.00845. Kalyuzhnyi Y. V., Hlushak S. P. Phase coexistencein polydisperse multi-Yukawa hard-sphere fluid: hightemperature approximation. The Journal of ChemicalPhysics. 2006;125(3): 034501. DOI: https://doi.org/10.1063/1.221241946. Mondal C., Sengupta S. Polymorphism,thermodynamic anomalies, and network formation inan atomistic model with two internal states. PhysicalReview E. 2011;84(5): 051503. DOI: https://doi.org/10.1103/PhysRevE.84.05150347. Bonn D., Denn M. M., Berthier L., Divoux T.,Manneville S. Yield stress materials in soft condensedmatter. Reviews of Modern Physics. 2017;89(3): 035005.DOI: https://doi.org/10.1103/RevModPhys.89.03500548. Tanaka H. Two-order-parameter model of theliquid–glass transition. I. Relation between glasstransition and crystallization. Journal of Non-Crystalline Solids. 2005;351(43-45): 3371–3384. DOI:https://doi.org/10.1016/j.jnoncrysol.2005.09.00849. Balesku R. Ravnovesnaya i neravnovesnayastatisticheskaya mekhanika [Equilibrium and nonequilibriumstatistical mechanics]. Moscow: Mir Publ.;1978. vol. 1. 404 c. (In Russ.)50. Chari S., Inguva R., Murthy K. P. N. A newtruncation scheme for BBGKY hierarchy: conservationof energy and time reversibility. arXiv preprintarXiv: 1608. 02338. DOI: https://arxiv.org/abs/1608.0233851. Gallagher I., Saint-Raymond L., Texier B. FromNewton to Boltzmann: hard spheres and short-rangepotentials. European Mathematical Society.arXiv:1208.5753. DOI: https://arxiv.org/abs/1208.575352. Rudzinski J. F., Noid W. G. A generalized-Yvon-Born-Green method for coarse-grained modeling. TheEuropean Physical Journal Special Topics. 224(12),2193–2216. DOI: https://doi.org/10.1140/epjst/e2015-02408-953. Franz B., Taylor-King J. P., Yates C., Erban R.Hard-sphere interactions in velocity-jump models.Physical Review E. 2016;94(1): 012129. DOI: https://doi.org/10.1103/PhysRevE.94.01212954. Gerasimenko V., Gapyak I. Low-Densityasymptotic behavior of observables of hard spherefluids. Advances in Mathematical Physics. 2018:6252919. DOI: https://doi.org/10.1155/2018/625291955. Lue L. Collision statistics, thermodynamics,and transport coefficients of hard hyperspheres inthree, four, and five dimensions. The Journal ofChemical Physics. 2005;122(4): 044513. DOI: https://doi.org/10.1063/1.183449856. Cigala G., Costa D., Bomont J. M., Caccamo C.Aggregate formation in a model fluid with microscopicpiecewise-continuous competing interactions.Molecular Physics. 2015;113(17–18): 2583–2592.DOI: https://doi.org/10.1080/00268976.2015.107800657. Jadrich R., Schweizer K. S. Equilibrium theoryof the hard sphere fluid and glasses in the metastableregime up to jamming. I. Thermodynamics. The Journalof Chemical Physics. 2013;139(5): 054501. DOI: https://doi.org/10.1063/1.481627558. Mondal A., Premkumar L., Das S. P. Dependenceof the configurational entropy on amorphousstructures of a hard-sphere fluid. Physical Review E.2017;96(1): 012124. DOI: https://doi.org/10.1103/PhysRevE.96.01212459. Sasai M. Energy landscape picture ofsupercooled liquids: application of a generalizedrandom energy model. The Journal of Chemical Physics.2003;118(23): 10651–10662. DOI: https://doi.org/10.1063/1.157478160. Sastry S. Liquid limits: Glass transition andliquid-gas spinodal boundaries of metastable liquids.Physical Review Letters. 2000;85(3): 590. DOI: https://doi.org/10.1103/PhysRevLett.85.59061. Uche O. U., Stillinger F. H., Torquato S. On therealizability of pair correlation functions. Physica A:Statistical Mechanics and its Applications. 2006;360(1):21–36. DOI: https://doi.org/10.1016/j.physa.2005.03.05862. Bi D., Henkes S., Daniels K. E., Chakraborty B.The statistical physics of athermal materials. Annu.Rev. Condens. Matter Phys. 2015;6(1): 63–83. DOI:https://doi.org/10.1146/annurev-conmatphys-031214-01433663. Bishop M., Masters A., Vlasov A. Y. Higher virialcoefficients of four and five dimensional hardhyperspheres. The Journal of Chemical Physics.2004;121(14): 6884–6886. DOI: https://doi.org/10.1063/1.177757464. Sliusarenko O. Y., Chechkin A. V., SlyusarenkoY. V. The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for manybodydissipative randomly driven systems. Journal ofMathematical Physics. 2015;56(4): 043302. DOI:https://doi.org/10.1063/1.491861265. Tang Y. A new grand canonical ensemblemethod to calculate first-order phase transitions. TheJournal of chemical physics. 2011;134(22): 224508. DOI:https://doi.org/10.1063/1.359904866. Tsednee T., Luchko T. Closure for the Ornstein-Zernike equation with pressure and free energyconsistency. Physical Review E. 2019;99(3): 032130.DOI: https://doi.org/10.1103/PhysRevE.99.03213067. Maimbourg T., Kurchan J., Zamponi, F. Solutionof the dynamics of liquids in the large-dimensionallimit. Physical review letters. 2016;116(1): 015902. DOI:https://doi.org/10.1103/PhysRevLett.116.01590268. Mari, R., & Kurchan, J. Dynamical transition ofglasses: from exact to approximate. The Journal ofChemical Physics. 2011;135(12): 124504. DOI: https://doi.org/10.1063/1.362680269. Frisch H. L., Percus J. K. High dimensionalityas an organizing device for classical fluids. PhysicalReview E. 1999;60(3): 2942. DOI: https://doi.org/10.1103/PhysRevE.60.294270. Finken R., Schmidt M., Löwen H. Freezingtransition of hard hyperspheres. Physical Review E.2001;65(1): 016108. DOI: https://doi.org/10.1103/PhysRevE.65.01610871. Torquato S., Uche O. U., Stillinger F. H. Randomsequential addition of hard spheres in high Euclideandimensions. Physical Review E. 2006;74(6): 061308.DOI: https://doi.org/10.1103/PhysRevE.74.06130872. Martynov G. A. Fundamental theory of liquids;method of distribution functions. Bristol: Adam Hilger;1992, 470 p.73. Vompe A. G., Martynov G. A. The self-consistentstatistical theory of condensation. The Journal ofChemical Physics. 1997;106(14): 6095–6101. DOI:https://doi.org/10.1063/1.47327274. Krokston K. Fizika zhidkogo sostoyaniya.Statisticheskoe vvedenie [Physics of the liquid state.Statistical introduction]. Moscow: Mir Publ.; 1978.400 p. (In Russ.)75. Rogers F. J., Young D. A. New, thermodynamicallyconsistent, integral equation for simple fluids. PhysicalReview A. 1984;30(2): 999. DOI: https://doi.org/10.1103/PhysRevA.30.99976. Wertheim M. S. Exact solution of the Percus–Yevick integral equation for hard spheres Phys. Rev.Letters. 1963;10(8): 321–323. DOI: https://doi.org/10.1103/PhysRevLett.10.32177. Tikhonov D. A., Kiselyov O. E., Martynov G. A.,Sarkisov G. N. Singlet integral equation in thestatistical theory of surface phenomena in liquids. J.of Mol. Liquids. 1999;82(1–2): 3– 17. DOI: https://doi.org/10.1016/S0167-7322(99)00037-978. Agrafonov Yu., Petrushin I. Two-particledistribution function of a non-ideal molecular systemnear a hard surface. Physics Procedia. 2015;71. 364–368. DOI: https://doi.org/10.1016/j.phpro.2015.08.35379. Agrafonov Yu., Petrushin I. Close order in themolecular system near hard surface. Journal of Physics:Conference Series. 2016;747: 012024. DOI: https://doi.org/10.1088/1742-6596/747/1/01202480. He Y., Rice S. A., Xu X. Analytic solution of theOrnstein-Zernike relation for inhomogeneous liquids.The Journal of Chemical Physics. 2016;145(23): 234508.DOI: https://doi.org/10.1063/1.497202081. Agrafonov Y. V., Petrushin I. S. Usingmolecular distribution functions to calculate thestructural properties of amorphous solids. Bulletinof the Russian Academy of Sciences: Physics. 2020;84:783–787. DOI: https://doi.org/10.3103/S106287382007003582. Bertheir L., Ediger M. D. How to “measure” astructural relaxation time that is too long to bemeasured? arXiv:2005.06520v1. DOI: https://arxiv.org/abs/2005.0652083. Karmakar S., Dasgupta C., Sastry S. Lengthscales in glass-forming liquids and related systems: areview. Reports on Progress in Physics. 2015;79(1):016601. DOI: https://doi.org/10.1088/0034-4885/79/1/01660184. De Michele C., Sciortino F., Coniglio A. Scalingin soft spheres: fragility invariance on the repulsivepotential softness. Journal of Physics: CondensedMatter. 2004;16(45): L489. DOI: https://doi.org/10.1088/0953-8984/16/45/L0185. Niblett S. P., de Souza V. K., Jack R. L., Wales D. J.Effects of random pinning on the potential energylandscape of a supercooled liquid. The Journal ofChemical Physics. 2018;149(11): 114503. DOI: https://doi.org/10.1063/1.504214086. Wolynes P. G., Lubchenko V. Structural glassesand supercooled liquids: Theory, experiment, andapplications. New York: John Wiley & Sons; 2012. 404p. DOI: https://doi.org/10.1002/978111820247087. Jack R. L., Garrahan J. P. Phase transition forquenched coupled replicas in a plaquette spin modelof glasses. Physical Review Letters. 2016;116(5): 055702.DOI: https://doi.org/10.1103/PhysRevLett.116.05570288. Habasaki J., Ueda A. Molecular dynamics studyof one-component soft-core system: thermodynamicproperties in the supercooled liquid and glassy states.The Journal of Chemical Physics. 2013;138(14): 144503.DOI: https://doi.org/10.1063/1.479988089. Bomont J. M., Hansen J. P., Pastore G. Aninvestigation of the liquid to glass transition usingintegral equations for the pair structure of coupledreplicae. J. Chem. Phys. 2014;141(17): 174505. DOI:https://doi.org/10.1063/1.490077490. Parisi G., Urbani P., Zamponi F. Theory of SimpleGlasses: Exact Solutions in Infinite Dimensions.Cambridge: Cambridge University Press; 2020. 324 p.DOI: https://doi.org/10.1017/978110812049491. Robles M., López de Haro M., Santos A., BravoYuste S. Is there a glass transition for dense hardspheresystems? The Journal of Chemical Physics.1998;108(3): 1290–1291. DOI: https://doi.org/10.1063/1.47549992. Grigera T. S., Martín-Mayor V., Parisi G.,Verrocchio P. Asymptotic aging in structural glasses.Physical Review B, 2004;70(1): 014202. DOI: https://doi.org/10.1103/PhysRevB.70.01420293. Vega C., Abascal J. L., McBride C., Bresme F.The fluid–solid equilibrium for a charged hard spheremodel revisited. The Journal of Chemical Physics.2003; 119 (2): 964–971. DOI: https://doi.org/10.1063/1.157637494. Kaneyoshi T. Surface amorphization in atransverse Ising nanowire; effects of a transverse field.Physica B: Condensed Matter. 2017;513: 87–94. DOI:https://doi.org/10.1016/j.physb.2017.03.01595. Paganini I. E., Davidchack R. L., Laird B. B.,Urrutia I. Properties of the hard-sphere fluid at a planarwall using virial series and molecular-dynamicssimulation. The Journal of Chemical Physics. 2018;149(1):014704. DOI: https://doi.org/10.1063/1.502533296. Properzi L., Santoro M., Minicucci M., Iesari F.,Ciambezi M., Nataf L., Di Cicco A. Structural evolutionmechanisms of amorphous and liquid As2 Se3 at highpressures. Physical Review B. 2016;93(21): 214205. DOI:https://doi.org/10.1103/PhysRevB.93.21420597. Sesé L. M. Computational study of the meltingfreezingtransition in the quantum hard-sphere systemfor intermediate densities. I. Thermodynamic results.The Journal of Chemical Physics. 2007;126(16): 164508.DOI: https://doi.org/10.1063/1.271852398. Shetty R., Escobedo F. A. On the application ofvirtual Gibbs ensembles to the direct simulation offluid–fluid and solid–fluid phase coexistence. TheJournal of Chemical Physics. 2002;116(18): 7957–7966.DOI: https://doi.org/10.1063/1.1467899

In this work the role of disorder, interaction and temperature in the physics of quantum non-ergodic systems is discussed. I first review what is meant by thermalization in closed quantum systems, and how ergodicity is violated in the presence of strong disorder, due to the phenomenon of Anderson localization. I explain why localization can be stable against the addition of weak dephasing interactions, and how this leads to the very rich phenomenology associated with many-body localization. I also briefly compare localized systems with their closest classical analogue, which are glasses, and discuss their similarities and differences, the most striking being that in quantum systems genuine non ergodicity can be proven in some cases, while in classical systems it is a matter of debate whether thermalization eventually takes place at very long times. Up to now, many-body localization has been studies in the region of strong disorder and weak interaction. I show that strongly interacting systems display phenomena very similar to localization, even in the absence of disorder. In such systems, dynamics starting from a random inhomogeneous initial condition are non-perturbatively slow, and relaxation takes place only in exponentially long times. While in the thermodynamic limit ergodicity is ultimately restored due to rare events, from the practical point of view such systems look as localized on their initial condition, and this behavior can be studied experimentally. Since their behavior shares similarities with both many-body localized and classical glassy systems, these models are termed “quantum glasses”. Apart from the interplay between disorder and interaction, another important issue concerns the role of temperature for the physics of localization. In non-interacting systems, an energy threshold separating delocalized and localized states exist, termed “mobility edge”. It is commonly believed that a mobility edge should exist in interacting systems, too. I argue that this scenario is inconsistent because inclusions of the ergodic phase in the supposedly localized phase can serve as mobile baths that induce global delocalization. I conclude that true non-ergodicity can be present only if the whole spectrum is localized. Therefore, the putative transition as a function of temperature is reduced to a sharp crossover. I numerically show that the previously reported mobility edges can not be distinguished from finite size effects. Finally, the relevance of my results for realistic experimental situations is discussed.

Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation  even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition. Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario. For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$. Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role. Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.

QC 20150306

La description détaillée des systèmes désordonnés et vitreux représente un défi central en physique statistique et de la matière condensée, puisqu'à ce jour il n'existe pas de théorie unique et établie permettant de comprendre ces systèmes, pourtant omniprésents.Ce travail de recherche est lié en particulier à l'étude des matériaux vitreux à basse température. Plus précisément, si l'on considère des systèmes formés par un ensemble de particules athermiques avec des interactions répulsives de portée finie, en augmentant la densité, on peut observer une transition dite d'encombrement ("jamming"). Celle-ci consiste en un blocage des degrés de liberté accompagné par une augmentation spectaculaire de la rigidité du matériau.Nous étudierons ce problème à l’aide d’une analogie formelle entre des modèles de sphères et le perceptron, un modèle théorique qui développe une transition d'encombrement et des phénomènes de frustration typiques des systèmes désordonnés.En tant que modèle en champ moyen, il permet d'obtenir des résultats analytiques précis et généralisables à des systèmes à haute dimension.L'enjeu majeur de cette étude est de reconstruire le spectre des modes de vibration et toutes les propriétés pertinentes d'une phase spécifique (correspondant au régime dit des sphères dures).Dans ce cadre, nous dériverons le potentiel effectif en fonction des paramètres d'ordre du modèle et nous montrerons qu'il est dominé à proximité du point de jamming par une interaction logarithmique non triviale, qui clarifiera le lien entre les forces de contact et les distances moyennes entre les particules, dans la région critique et au-delà.Comprendre pleinement la transition d'encombrement et les propriétés du perceptron nous permettra de faire des progrès dans plusieurs domaines reliés. En premier lieu, cela peut conduire à une théorie complète des systèmes amorphes, à la fois en dimension infinie et en dimension finie.De plus, le modèle du perceptron semble avoir un lien étroit avec des problèmes dits de Von Neumann. En effet, les systèmes biologiques et écologiques développent souvent des propriétés liées à une condition pseudo-critique en mettant en oeuvre des mécanismes d'optimisation de ressource-consommation.Est-il possible d'identifier un régime caractérisé par une brisure de symétrie? Quel serait le spectre de fluctuations d'énergie dans ces systèmes?Ce ne sont que quelques-unes des questions auxquelles nous essayerons de répondre dans cette thèse.Cependant, l'approximation de champ moyen peut parfois fournir des informationsincorrectes ou trompeuses, en particulier dans l'étude de certaines transitions de phase et la détermination des dimensions critiques inférieure et supérieure.Afin d'avoir une vue d'ensemble et pouvoir manipuler correctement des systèmes en dimension finie, dans la suite de la thèse nous discuterons comment obtenir un développement perturbatif systématique, applicable à tout modèle, à condition que ce dernier soit défini sur un réseau ou un graphe biparti.Notre motivation est en particulier liée à la possibilité d'étudier certaines transitions de phase du second ordre qui existent sur le réseau de Bethe - c'est-à-dire un réseau en arbre sans boucles dont chaque noeud a une connectivité fixe - mais qui sont qualitativement différentes ou absentes dans le modèle entièrement connecté correspondant
The detailed description of disordered and glassy systems represents an open problem in statistical physics and condensed matter. As yet, there is no single, well-established theory allowing to understand such systems. The research presented in this thesis is related in particular to the study of glassy materials in the low-temperature regime. More precisely, considering systems formed by athermal particles subject to repulsive short-range interactions, upon progressively increasing the density, a so-called jamming transition can be detected. It entails a freezing of the degrees of freedom and hence a huge increase of the material rigidity.We shall study this problem in view of a formal analogy between sphere models and the perceptron, a theoretical model undergoing a jamming transition and frustration phenomena typical of disordered systems. Being a mean-field model, it allows to obtain exact analytical results, which are generalizable to more complex high-dimensional settings.The main aim is to reconstruct the vibrational spectrum and all the relevant properties of a specific phase of the perceptron, corresponding to the hard-sphere regime.In this framework, we will derive the effective potential as a function of the gaps between and forces among the particles, and we will show that it is dominated by a non-trivial logarithmic interaction near the jamming point. This interaction in turn will clarify the relations existing between the relevant variables of the system, in the critical jamming region and beyond.Understanding the jamming transition and the perceptron properties will allow us to make progress in several related fields. First, this study could lay part of the groundwork towards a complete theory of amorphous systems, in both infinite and finite dimensions. Furthermore, the perceptron model seems to a have a close connection with the so-called Von Neumann problems. Indeed, biological and ecological systems often develop pseudo-critical properties and give rise to general mechanisms of resource-consumption optimisation.Is the identification of a broken symmetry regime possible? What would it yield in terms of the spectrum of the energy fluctuations?These are just a few questions we shall attempt to answer in this context.However, the mean-field approximation can sometimes provide wrong or misleading information, especially in studying certain phase transitions and determining the exact lower and upper critical dimensions. To have a broad perspective and correctly deal with finite-dimensional systems, in the second part of the thesis we will discuss obtaining a systematic perturbative expansion which can be applied to any model, as long as defined on a lattice or a bipartite graph.Our motivation is in particular due to the possibility of studying relevant second-order phase transitions which exist on the Bethe lattice — a lattice with a locally tree-like structure and fixed connectivity for each node — but which are qualitatively different or absent in the corresponding fully-connected version