Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

Geometric analysis of φ4 fields and Ising models. Parts I and II

Abstract: We provide here the details of the proof, announced in [1], that ind>4 dimensions the (even) φ4 Euclidean field theory, with a lattice cut-off, is inevitably free in the continuum limit (in the single phase regime). The analysis is nonperturbative, and is based on a representation of the field variables (or spins in Ising systems) as source/sink creation operators in a system of random currents — which may be viewed as the mediators of correlations. In this dual representation, the onset of long-range-order is attributed to percolation in an ensemble of sourceless currents, and the physical interaction in the φ4 field — and other aspects of the critical behavior in Ising models — are directly related to the intersection properties of long current clusters. An insight into the criticality of the dimensiond=4 is derived from an analogy (foreseen by K. Symanzik) with the intersection properties of paths of Brownian motion. Other results include the proof that in certain respect, the critical behavior in Ising models is in exact agreement with the mean-field approximation in high dimensionsd>4, but not in the low dimensiond=2 — for which we establish the “universality” of hyperscaling.

Ordering in strongly fluctuating condensed matter systems

Abstract: Ordering in Strongly Fluctuating Systems: Introductory Comments.- 1. Introduction.- 2. A Theorist's Ideal Glass.- 3. Systems Far From Equilibrium.- Phase Transitions in Low-Dimensional Systems and Renormalization Group Theory.- 1. Phase Transitions and Some Simple Spin Models.- 2. Fluctuations and the Lower Critical Dimension.- 3. Values of Lower Critical Dimensionality for Some Spin Models.- 4. Fluctuations.- 5. Introduction to the Renormalization Group.- Real-Space Renormalization-Group Method for Quantum Systems.- Upper Marginal Dimensionality, Concept and Experiment.- 1. Phenomenological Description.- 2. Mean Field Theory.- 3. Ginzburg Criterion.- 4. Experiments on LiTbF4.- 5. Conclusion.- Lower Marginal Dimensionality. X-Ray Scattering from the Smectic-A Phase of Liquid Crystals.- 1. Introduction.- 2. The Nematic and Smectic A Phases of Liquid Crystals.- 3. The Correlation Function in the Harmonic Approximation.- 4. Experiment and Analysis.- 5. Results and Conclusions.- Appendix: Calculation of $$$$ in the SmA Phase.- Critical Fluctuations Under Shear Flow.- 1. Turbidity: TC change.- 2. The scattered light: Anisotropy mean-field lowering of UCD?.- 3. Discussion.- 4. "Moralite".- Lifshitz Points in Ising Systems with Competing Interactions.- 1. Introduction.- 2. One-dimensional Ising Systems with competing Interactions.- 3. Two-dimensional Ising systems.- 4. Conclusions.- Elementary Excitations in Magnetic Chains.- 1. Introduction.- 2. Magnons in XY-like Magnetic Chains.- 3. The Anisotropic, Classical XY Chain.- 3.1 The Model.- 3.2 Intuitive Analysis at Low Temperature for q = 2 and J = 0.- 3.3 Energy of a Wall.- 3.4 Number of Walls.- 3.5 Antiferromagnets in a Magnetic Field.- 4. A Simple Dynamical Model: The Almost - Ising Antiferromagnetic Chain.- 4.1 The Model.- 4.2 Collisions Between Two Solitons.- 5. Propagation of Broad Walls.- Experimental Studies of Linear and Nonlinear Modes in 1-D-Magnets.- 1. Real Systems Experimental Methods.- 2. Linear Excitations.- 3. Nonlinear Excitations.- Q-Dependence of the Soliton Response in CsNiF3 At.- T = 10K and H =5kG.- Dynamics of the Sine-Gordon Chain: The Kink-Phonon Interaction, Soliton Diffusion and Dynamical Correlations.- 1. Statement of the Problem.- 2. A Kink-Phonon Collision.- 3. Diffusive Motion of the Kink.- 4. Dynamical Correlation Functions.- The Spin-Wave Continuum of the S=1/2 Linear Heisenberg Antiferrornagnet.- Excitations and Phase Transitions in Random Anti-Ferromagnets.- Neutron Scattering.- Critical Phenomena at Phase Transitions.- Percolation.- Excitations of Dilute Magnets Near the Percolation Threshold.- Critical Properties of the Mixed Ising Ferromagnet.- Structure and Phase Transitions in Physisorbed Monolayers.- History and Background.- Statistical Thermodynamics of Physical Adsorption.- Structural Investigations of Monolayers.- Substrate Influences.- Commensurate-Incommensurate Transition and Orientational Epitaxy.- Antiferromagnetism in 0" Films.- Conclusion.- Two-Dimensional Solids and Their Interaction with Substrates.- I. Collective Phenomena and Phase Transitions in Two Dimensions.- 1.1 Early Theoretical Works.- 1.2 Experimental Situation.- II. Effect of Substrate.- II.1 Two-Dimensional Solids and Adsorbed Layers.- II.2 Substrate Distortion and Related Effects.- II.3 Chemical Potential.- II.4 Substrate Potential.- II.5 Conclusion.- III. Walls and Domains.- III.1 A One-Dimensional Model.- III.2 The Theory of Frank and Van der Merwe.- III.3 Aubry's Theory.- III.4 Domains and Walls for Dimensions Larger than 1.- IV. The Pokrovskii-Talapov Model.- IV.1 Hypotheses.- IV.2 Solution.- IV.3 Bragg Singularities.- IV.4 The Pinning Transition.- V. Rate Gas Monolayers on Graphite or Lamellar Halides.- V.1 Introduction.- V.2 The Zero Temperature Theory of Bak, Mukamel, Villain and Wentowska.- V.3 Rare Gas Monolayers on Hexagonal Substrates at T i 0.- V.4 Effect of Substrate Distortions.- VI. The Novaco-Mc Tague Orientational Instability.- VI.1 General Argument.- VI.2 Case of Parallel Walls.- VI.3 Case of a Regular Network of Intersecting Walls.- VI.4 Finite Temperatures.- VI.5 Microscopic Theories.- Appendix A. Bragg Singularities of a 2-D, Harmonic Crystal.- Appendix B. Interaction between two Solutions.- Appendix C. Partition function of the Pokrovskii-Talapov Model Near the Commensurable-Incommensurable Transition.- Appendix D. Bragg Singularities of the Pokrovskii-Talapov Model Near the C-I Transition.- Appendix E. The Roughening Transition.- The Dislocation Theory of Melting: History, Status and Prognosis.- 1. Introduction.- 2. History.- 3. Status.- 4. Prognosis.- The Kosterlitz-Thouless Theory of Two-Dimensional Melting.- Phase Transitions and Orientational Order in a Two-Dimensional Lennard-Jones System.- The Roughening Transition.- I. Introduction.- II. The solid-On-Solid Model.- III. The BCF Argument.- IV. Experimental Results.- V. Monte Carlo Calculations: Qualitative Features.- VI. Static Critical Behavior.- VII. Roughening Dynamics and the Kosterlitz Renormalization Group Method.- VIII.The FSOS Model and Mc Calculations.- IX. Final Remarks.- Statics and Dynamics of the Roughening Transition: A Self-Consistent Calculation.- I. Introduction.- II. Roughening Transition.- III. Two-Dimensional Planar Model.- IV. Conclusions.- Fluctuations in Two-Dimensional Six-Vertex Systems.- Light Scattering Studies of the Two-Dimensional Phase Transition in Squaric Acid.- 1. Introduction.- 2. Light Scattering Studies.- 3. Order Parameter.- 4. Order Flucatuations.- 5. Peak Shape and Width.- 6. Disorder Induced Scattering.- 7. Conclusions.- Monte Carlo Simulation of Dilute Systems and of Two-Dimensional Systems.- I. Introduction.- II. Ferromagnets Diluted with Nonmagnetic Impurities and Related Systems.- III. Models for Quasi-Two-Dimensional (2D) Magnets.- IV. Lattice Gas Models for Adsorbed Monolayers at Surfaces.- Order and Fluctuations in Smectic Liquid Crystals.- I. Introduction.- II. The Nematic Phase.- III.The Nematic-Smectic A Transition and The Smectic A Phase.- IV. The Smectic C Phase and Smc-SmA Transition.- v. Liquid Crystals and Lower Dimensional Physics.- Dislocations and Disclinations in Smectic Systems.- Translational Defects.- Orientational Defects.- Non-Elementary Defects.- Observation of Dislocations.- Dislocation Motion.- "Pair Creation" of Disclinations.- Defects and Phase Transitions.- Fluctuations and Freezing in a One-Dimensional Liquid:Hg3-?AsF6.- The Model Hamiltonian.- High Temperature Properties (T > TC).- Long Range Order.- Dynamics.- The Effect of Pressure on the Modulated Phases of TTF-TCNQ.- Spin Glasses A Brief Review of Experiments, Theories, and Computer Simulations.- 1. Spin Glass Materials and Experiments.- 2. Theoretical Models and Concepts.- 3. Spin-Glass Freezing: Phase Transition or Nonequilibrium Effect?.- 4. Conclusions and Outlook.- Random Anisotropy Spin-Glass.- Exact Results for a One-Dimensional Random-Anisotropy Spin Glass.- On Critical Slowing-down in Spin Glasses.- Participants.

Superposition approximation and natural iteration calculation in cluster‐variation method

Abstract: In the cluster‐variation method of cooperative phenomena and also in the quasichemical method, the bottleneck step has been to solve simultaneous equations. This paper proposes a new iterative procedure for solving the equations. This iteration does not use differentiation nor matrix inversion and may be called the natural iteration method. The free energy always decreases as the iteration proceeds, with a consequence that the iteration always converges to a stable solution (a local minimum of free energy) as long as the initial state is a physically acceptable one. The method derives in its introductory step a superposition approximation which writes the distribution variables of the basic cluster as a product of those of subclusters. The method is first explained with the pair approximation of the Ising ferromagnet, and then is applied to the fcc binary alloys to derive a phase diagram which is compared with the one reported recently by van Baal.

Introduction to the functional renormalization group

Abstract: I Foundations of the renormalization group.- Phase Transitions and the Scaling Hypothesis.- Mean-Field Theory and the Gaussian Approximation.- Wilsonian Renormalization Group.- Critical Behavior of the Ising Model Close to Four Dimensions.- Field-Theoretical Renormalization Group.- II Introduction to the functional renormalization group.- Functional Methods.- Exact FRG Flow Equations.- Vertex Expansion.- Derivative Expansion.- III Functional renormalization group approach to fermions.- Fermionic Functional Renormalization Group.- Normal Fermions: Partial Bosonization in the Forward Scattering Channel.- Superfluid Fermions: Partial Bosonization in the Particle-Particle Channel.