Academic literature on the topic 'Diluted spin systems'

We study diluted spin glass models in arbitrary dimension, where each spin interacts with a finite number of other spins chosen at random with a probability decaying to zero over some distance γ-1. For systems with pairwise interactions we show that the infinite-volume free energy converges to that of the mean-field Viana–Bray model,1 in the Kac limit γ→0. For p-spin like models we get only one bound: the free-energy is bounded from above by the one of the mean-field diluted p-spin.

We study the phase transitions and critical phenomena in 3D site-diluted (with nonmagnetic impurities) Potts model with spin states q=4 by Monte-Carlo method. The systems with linear sizes L=20-32 and spin concentrations p=1.00, 0.90, 0.65 are examined. Using the Binder cumulants method the forth order it is shown that the second-order phase transition is observed in strongly diluted model at spin concentration p=0.65; the pure model (p=1.00) and weakly diluted one (p=0.90) reveals the first-order phase transition. On the basis of finite-size scaling theory the static critical parameters of heat capacity, susceptibility, magnetization, and correlation length exponent are calculated.

Etude par mesures de susceptibilite magnetique et d'aimantation du systeme du titre. Ce compose stratifie est un systeme d'ising 3d. On etudie le diagramme de phase et on met un comportement de verre de spin. Pour x=0,72, les mesures montrent l'importance du comportement reentrant. L'analyse du comportement critique pour x=0,35 est analyse par l'etude de l'aimantation non lineaire. Mise en evidence d'une transition de phase. Valeur des exposants critiques. On compare ensuite le comportement avec celui des systemes bidimensionnels d'ising

In this work, I present nuclear probe spectroscopy studies, in detail, µ+SR and 57Fe-Mössbauer spectroscopy on solid-state systems with localized magnetic moments of 3d transition-metal ions supported by density functional theory calculations. Local probes are able to extract local quantities, e.g. the spin dynamics of the 57Fe site or the local, mostly interstitial µ+ site to distinguish between di_erent magnetic phases. The density functional theory calculations help to identify the muon site position from which the local quantity depends. My µ+SR studies on frustrated 3d magnets with quenched disorder concern the physics of phase transitions, avoided order-by-disorder, quantum uctuations or the appearance of spin-liquid-by-disorder. µ+SR is able to identify quantum spinliquid-like ground states without symmetry breaking or static magnetic order by the magnetic field at the muon site. BaTi0.5Mn0.5O3 is a magnetically highly-frustrated double perovskite with quenched disorder.It shows no freezing temperature or no frequency dependence of x1as expected for a spin glass. Microscopically, it is proposed that local interactions between magnetic orphan spins, dimers, and magnetic trimers of Mn4+ play an important role. The µ+SR experiment on BaTi0.5Mn0.5O3 shows an increase of the dynamical muon spin relaxation rate below 3 K which saturates down to 0.019 K coexisting with residual short-range magnetic order (<20% of the signal). A clear difference is observed in comparison with the classical cluster-spin glass SrTi0.5Mn0.5O3 which shows a peak of the zero-field muon spin relaxation rate: a persistent low-energy spin dynamics is present in BaTi0.5Mn0.5O3 down to 20 K. My DFT calculations propose a positive muon site insight the Ba plane close to O atoms. Here, a slight preference of the muon site close to Mn4+ is possible which could put the muon close the orphan spins, dimers, and magnetic trimers, respectively, avoiding the nonmagnetic Ti4+ face-sharing octahedra. Theoretically, a specific ground state of BaTi0.5Mn0.5O3 is not proposed. A clear discrimination between a quantum spin liquid ground state and a mimicry state with the appearance of spin-liquid-by-disorder is not possible from the existing data. I present a µ+SR study on the bond-disordered magnetically highly frustrated pyrochlore fluoride NaCaCo2F7. Neutron spectroscopy studies on NaCaCo2F7 revealed static short-range order consistent with a continuous manifold of cluster-like states being a superposition of noncoplanar ψ2(m3z2-r2) and coplanar ψ3(mx2-y2) states with a correlation length of around 16Å. No evidence for static magnetic long-range order is found in NaCaCo2F7 probed by µ+SR confirming the absence of an order-by-disorder mechanism. The experimental results are not consistent with a classical local-planar XY cluster-spin glassiness. In these µSR experiments, two muon sites are observed. The relative occupancy of both muon sites is nearly temperature independent. Muon site I is a collinear diamagnetic F-µ+-F bound state pulling two F- close towards the muon revealed by the muon spin time evolution. To investigate the pure F-µ+-F bound state in a broad temperature range I have performed an additional µ+SR study on CaF2. This study solved open questions of muon diffusion around 290 K which was observed in NaCaCo2F7 as well. The F-µ+-F spin relaxation indicates the slowing down of the magnetic Co2+ spin fluctuations upon cooling towards the NMR spin freezing temperature Tf≈ 2.4 K. The relaxation rate saturates below 800 mK and remains constant down to 20 mK. The dominant part of the magnetic short-range relaxation signal is a dynamical relaxation as probed by longitudinal magnetic-field experiments. Muon site II exhibits a strong dynamical relaxation rate at 290 K and below and shows persistent µ+ spin dynamics down to 20 mK. Qualitatively, muon site II shows persistent µ+ spin dynamics with one order of magnitude higher dynamical relaxation rates compared to muon site I. DFT calculations of a comparison of the unperturbed unit cells of NaCaCo2F7 and NaCaNi2F7, which has shown just one muon site experimentally, are consistent with a decrease of the energy differences of energy minima and support the experimentally observed muon site ambivalence. In summary, the µ+SR studies propose NaCaCo2F7 as a quantum cluster-spin glass candidate. I present a systematic 57Fe-Mössbauer study on highly diluted Fe centers in Li2(Li1-xFex)N as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Here, Fe is embedded in an α-Li3N matrix. The oxidation state of Fe and possible ferromagnetic nature are in controversial discussions in the literature. Below 30 K the Fe centers exhibit a giant magnetic hyperfine field of BA=70.25(2) T parallel to the axis of strongest electric field gradient Vzz=-154.0(1) V / Å 2. This observation is consistent with a Fe1+d7 charge state with unquenched orbital moment and J=7/2. Fluctuations of the magnetic hyperfine field are observed between 50 K and 300 K and described by the Blume two-level relaxation model consistent with single-atomic magnetism as proven by the invariance of Blume relaxation parameters for the concentration tuning x< 0.025 excluding a ferromagnetic nature. From the temperature dependence of the fluctuation rate an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal-activation barrier of EA=570(6) K and an attempt frequency v0=309(10) GHz. Mössbauer spectroscopy studies with applied transverse magnetic fields up to 5 T reveal a large increase of the fluctuation rate by two orders of magnitude. In longitudinal magnetic fields a splitting of the fluctuation rate into two branches is observed. The experimental observations are qualitatively reproduced by a single-ion spin Hamiltonian analysis. It demonstrates that for dominant magnetic quantum tunneling relaxation processes a weak axial single-ion anisotropy D of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.

This chapter illustrates basic concepts of quantum integrable systems on two important models of statistical physics: the Q-state Potts model and the O(n) model. Both models are transformed into loop and vertex models that provide representations of the dense and dilute Temperley–Lieb algebras. The identification of the corresponding integrable R-matrices leads to the solution of both models by the algebraic Bethe Ansatz technique. Elementary excitations are discussed in the critical case and the link to conformal field theory in the thermodynamic limit is established. The concluding sections outline the solution of a specific model of the theta point of collapsing polymers, leading to a continuum limit with a non-compact target space.

In this chapter, we discuss adsorption phenomena in supercritical systems, a situation that occurs in many application areas in chemical-process and materials engineering. An example of a commercial application in this area, which has achieved wide acceptance as a tool in analytical chemistry, is supercritical fluid chromatography (SFC). Not only is SFC a powerful technique for chemical analysis, but it also is a useful method for measuring transportive and thermodynamic properties in the near-critical systems. In the next section, we analyze adsorption-column dynamics using simple dynamic models, and describe how data from a chromatographic column can be used to estimate various thermodynamic and transport properties.We then proceed to discuss the effects of proximity to the critical point on adsorption behavior in these systems. The closer the system is to its critical point, the more interesting is its behavior. For very dilute solute systems, like those considered here, the energy balance is often ignored to a first approximation; this leads to a simple set of mass-balance equations defining transport for each species. These equations can be developed to various levels of complexity, depending upon the treatment of the adsorbent (stationary phase). The conceptual view of these phases can span a wide range of possibilities ranging from completely nonporous solids (fused structures) to porous materials with complicated ill-defined pore structures. Given these considerations, it is customary to make the following assumptions in the development of a simple model of adsorber-bed dynamics: . . .1. The stationary and mobile phases are continuous in the direction of the flow, with the fluid phase possessing a flat velocity profile (“plug” flow).. . . . . . 2. The porosity of the stationary phase is considered constant irrespective of pressure and temperature conditions (i.e., it is incompressible). . . . . . .3. The column is considered to be radially homogeneous, leading to a set of equations with one spatially independent variable, representing distance along the column axis. . . . . . . 4. The dispersion term in the model equation represents the combined effects of molecular diffusion and dispersion due to convective stirring in the bed. These effects are combined into an effective phenomenological dispersion coefficient, considered to be constant throughout the column. . . .

Following a brief review of laser frequency and time domain techniques for overcoming inhomogeneous broadening of optical transitions in solids, recent studies on the failure of the optical Bloch equations (OBE) in describing saturation and coherent transient phenomena in ruby will be discussed. Experiments using free induction decay (FID), as in the original work on the system Pr3+:LaF3 by DeVoe and Brewer1, as well as extensions to rotary echos2 and hole-burning3 will be described. At low fields (~ 0.4 T), the time and frequency domain linewidth variation with Rabi frequency agree provided care is taken to avoid line broadening caused by spectral diffusion4. Recent work at high fields (~ 5 T), where Cr-Cr electron spin flipping is suppressed5, shows that spectral diffusion decreases and the dephasing time increases. Observed frequency domain hole widths as narrow as 18 kHz (FWHM) have been obtained for the 4 A2(−1/2)→E¯(−1/2) optical transition in dilute ruby using a pump-probe technique4. Work with such narrow holes emphasizes the fundamental limits imposed by the uncertainty principle and as an aside, a thought experiment where single photons are transmitted through "frequency slits" will be discussed.