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Auteur : Grafiati

Publié le 7 juillet 2024

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1

Chakrabarti, B. K. Quantum ising phases and transitions in transverse ising models. New York : Springer, 1996.

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2

Liebmann, R. Statistical mechanics of periodic frustrated Ising systems. Berlin : Springer-Verlag, 1986.

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3

Kremer, Sebastian. Oberflächendynamik im Q2R-Ising-Modell. Aachen : Verlag Shaker, 1992.

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4

MacFarland, T. Parallel simulation of the Ising model. Ithaca, N.Y : Cornell Theory Center, Cornell University, 1994.

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5

Baxter, Rodney J. Exactly solved models in statistical mechanics. London : Academic, 1989.

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6

Rychkov, Slava. Lectures on the Random Field Ising Model. Cham : Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-42000-9.

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7

Handrick, Klaus. Modelle zur Beschreibung magnetischer Wechselwirkungen zwischen paramagnetischen Zentren in niedrigdimensionalen Systemen. Aachen [Germany] : Shaker, 1992.

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8

Cerf, Raphaël. The Wulff crystal in Ising and percolation models : Ecole d'Ete de Probabilites de Saint-Flour XXXIV, 2004. Sous la direction de Picard Jean. Berlin : Springer, 2006.

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9

Jerrum, Mark. Polynomial-time approximation algorithms for the Ising model. Edinburgh : University of Edinburgh Department of Computer Science, 1990.

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10

A, Jackson Kenneth. Monte Carlo simulation of the rapid crystallization of bismuth-doped silicon. [Washington, D.C : National Aeronautics and Space Administration, 1997.

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11

Newman, M. E. J. Monte Carlo study of the random-field Ising model. Ithaca, N.Y : Cornell Theory Center, Cornell University, 1995.

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12

1930-, Lebowitz Joel Louis, dir. Simple models of equilibrium and nonequilibrium phenomena. Amsterdam : North-Holland, 1987.

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13

A, Jackson K., et United States. National Aeronautics and Space Administration., dir. Orientation and velocity dependence of the nonequilibrium partition coefficient. [Washington, DC : National Aeronautics and Space Administration, 1995.

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14

Prum, Bernard. Stochastic processes on a lattice and Gibbs measures. Dordrecht : Kluwer Academic Publishers, 1991.

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15

Barkema, G. T. Transient and asymptotic domain growth in the 3D Ising model with conserved spin. Ithaca, N.Y : Cornell Theory Center, Cornell University, 1994.

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16

Luijten, Erik. Interaction range, universality and the upper critical dimension. Delft, Netherlands : Delft University Press, 1997.

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17

W, Lovesey S., Rutherford Appleton Laboratory et Council For The Central Laboratory of The Research Councils., dir. A theory of spin correlations and neutron scattering from paramagnetic materials based on the Ising-Heisenberg model in one, two and three space dimensions. Chilton : Rutherford Appleton Laboratory, 1996.

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18

Ecole d'été de probabilités de Saint-Flour (27th 1997). Lectures on probability theory and statistics : Ecole d'été de probabilités de Saint-Flour XXVII, 1997. Sous la direction de Bertoin Jean, Martinelli F, Peres Y, Bernard P. 1944-, Bertoin Jean, Martinelli F et Peres Y. Berlin : Springer, 2000.

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19

Ecole d'été de probabilités de Saint-Flour (27th 1997). Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXVII, 1997. Sous la direction de Bertoin Jean, Martinelli F, Peres Y et Bernard P. 1944-. Berlin : Springer, 1999.

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20

McCoy, Barry M., et Tai Tsun Wu. Two-Dimensional Ising Model. Dover Publications, Incorporated, 2014.

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21

McKenzie, Donna G. Magnetic ordering in thin Ising bilayer systems. 1989.

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22

McCoy, Barry M., et Tai Tsun Wu. Two-Dimensional Ising Model : Second Edition. Dover Publications, Incorporated, 2014.

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23

Quantum Ising Phases and Transitions in Transverse Ising Models Lecture Notes in Physics. Springer, 2012.

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24

McCoy, Barry M. The two-dimensional Ising model. 2014.

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25

Shehadeh, Hayel. Monte Carlo studies of phase diagram and phase transitions of random, binary, SC, 3-D Ising model in magnetic field. 1989.

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26

Wu, Tai Tsun, et Barry McCoy. Two-Dimensional Ising Model. Harvard University Press, 2013.

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27

Wu, Wenhao. From classical to quantum glass. 1993.

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28

Luoma, Samuli. Introduction to the Ising Model. Nova Science Publishers, Incorporated, 2020.

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29

Cobbina, Francis. Monte Carlo study of a 3-D random binary magnetic Ising system possessing nearest- and next-nearest-neighbor interactions with no external field. 1989.

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30

Sikakana, Ike Qhubekani. Monte Carlo studies of a two-dimensional, binary, magnetic ising model with nearest-neighbor interactions. 1988.

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31

Cobbina, Francis. Monte Carlo study of a 3-D random binary magnetic Ising system possessing nearest- and next-nearest-neighbor interactions with no external field. 1989.

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32

Binek, Christian. Ising-Type Antiferromagnets : Model Systems in Statistical Physics and in the Magnetism of Exchange Bias. Springer Berlin / Heidelberg, 2010.

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33

Binek, Christian. Ising-type Antiferromagnets : Model Systems in Statistical Physics and in the Magnetism of Exchange Bias (Springer Tracts in Modern Physics). Springer, 2003.

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34

Palmer, John. Planar Ising Correlations (Progress in Mathematical Physics). Birkhäuser Boston, 2007.

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35

Baxter, Rodney J. Exactly Solved Models in Statistical Mechanics. Dover Publications, Incorporated, 2013.

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36

Baxter, Rodney J. Exactly Solved Models in Statistical Mechanics. Dover Publications, 2007.

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37

Baxter, Rodney J. Exactly Solved Models in Statistical Mechanics. Dover Publications, Incorporated, 2013.

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38

Baxter, Rodney J. Exactly Solved Models in Statistical Mechanics. Elsevier Science & Technology Books, 2016.

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39

King, David R. Monte Carlo study of the phase transitions for the 3-dimensional 4- and 6-state chiral clock models. 1993.

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40

Boudreau, Joseph F., et Eric S. Swanson. Classical spin systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0020.

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The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is then applied to the two-dimensional Ising model with the goal of determining the phase diagram for magnetization. Boundary conditions, the reweighting method, autocorrelation, and critical slowing down are all explored. Cluster algorithms for overcoming critical slowing down are developed next and shown to dramatically reduce autocorrelation. A variety of spin systems that illustrate first, second, and infinite order (topological) phase transitions are explored. Finally, applications to random systems called spin glasses and to neural networks are briefly reviewed.

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41

Chekhov, Leonid. Two-dimensional quantum gravity. Sous la direction de Gernot Akemann, Jinho Baik et Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.30.

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This article discusses the connection between large N matrix models and critical phenomena on lattices with fluctuating geometry, with particular emphasis on the solvable models of 2D lattice quantum gravity and how they are related to matrix models. It first provides an overview of the continuum world sheet theory and the Liouville gravity before deriving the Knizhnik-Polyakov-Zamolodchikov scaling relation. It then describes the simplest model of 2D gravity and the corresponding matrix model, along with the vertex/height integrable models on planar graphs and their mapping to matrix models. It also considers the discretization of the path integral over metrics, the solution of pure lattice gravity using the one-matrix model, the construction of the Ising model coupled to 2D gravity discretized on planar graphs, the O(n) loop model, the six-vertex model, the q-state Potts model, and solid-on-solid and ADE matrix models.

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42

Bertoin, J., F. Martinelli et Y. Peres. Lectures on Probability Theory and Statistics : Ecole d'Ete de Probabilites de Saint-Flour XXVII - 1997 (Lecture Notes in Mathematics). Springer, 2000.

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43

Rau, Jochen. Phase Transitions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199595068.003.0008.

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At a phase transition two or more different phases may coexist, such as vapour and liquid. Phase transitions can be classified according to their order. A phase transition is of first order if going from one phase to the other involves a discontinuous change in entropy, and, thus, a finite amount of latent heat; higher-order phase transitions do not involve latent heat but exhibit other types of discontinuities. This chapter investigates the necessary conditions for the coexistence of phases, and how phases are represented in a phase diagram. The order of a phase transition is defined with the help of the Ehrenfest classification. The chapter discusses the Clausius–Clapeyron relation which, for a first-order phase transition, relates the discontinuous changes in entropy and volume. Finally, this chapter considers the Ising ferromagnet as a simple model which exhibits a second-order phase transition. It also introduces the notion of an order parameter.

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44

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

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