Ising model

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

Probing Real-Space and Time-Resolved Correlation Functions with Many-Body Ramsey Interferometry

Abstract: We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time-resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover, they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We explicitly consider examples of the two-dimensional, antiferromagnetic Heisenberg model and the one-dimensional, long-range transverse field Ising model to illustrate the technique.

Studies on Phase Transitions by AC Calorimetry

Abstract: As examples of the best use of the so-called AC calorimetry technique, several results are described from various viewpoints. The behavior of heat capacity at ferroelectric, antiferroelectric and structural phase transitions is surveyed from the standpoint of critical behavior, of jump at first order transition, or of a sensitive metod of finding a new phase transition. In two- and three-dimensional antiferromagnets, the critical behavior is discussed with an emphasis on the crossover from the Ising to the Heisenberg system. In the two-dimensional antiferromagnets, the crossover is revealed from the dependence of the critical amplitude on the strength of the Ising-like anisotropy. A hyperscaling relation is proposed at nematic-to-smectic A transition of liquid crystals. Finally, studies of the frequency dependence of heat capacities in the denaturation of proteins and in the order-disorder transition of alloys are reported.

Gibbs Random Fields: Cluster Expansions

Abstract: 1. Gibbs Fields (Basic Notions).- 0 First Acquaintance with Gibbs Fields.- 1 Gibbs Modifications.- 2 Gibbs Modifications under Boundary Conditions and Definition of Gibbs Fields by Means of Conditional Distributions.- 2. Semi-Invariants and Combinatorics.- 1 Semi-Invariants and Their Elementary Properties.- 2 Hermite-Ito-Wick Polynomials. Diagrams. Integration by Parts.- 3 Estimates on Moments and Semi-Invariants of Functional of Gaussian Families.- 4 Connectedness and Summation over Trees.- 5 Estimates on Intersection Number.- 6 Lattices and Computations of Their Moebius Functions.- 7 Estimate of Semi-Invariants of Partially Dependent Random Variables.- 8 Abstract Diagrams (Algebraic Approach).- 3. General Scheme of Cluster Expansion.- 1 Cluster Representation of Partition Functions and Ensembles of Subsets.- 2 Cluster Expansion of Correlation Functions.- 3 Limit Correlation Function and Cluster Expansion of Measures.- 4 Cluster Expansion and Asymptotics of Free Energy. Analyticity of Correlation Functions.- 5 Regions of Cluster Expansions for the Ising Model.- 6 Point Ensembles.- 4. Small Parameters in Interactions.- 1 Gibbs Modifications of Independent Fields with Bounded Potential.- 2 Unbounded Interactions in the Finite-Range Part of a Potential.- 3 Gibbs Modifications of d-Dependent Fields.- 4 Gibbs Point Field in Rv.- 5 Models with Continuous Time.- 6 Expansion of Semi-Invariants. Perturbation of a Gaussian Field.- 7 Perturbation of a Gaussian Field with Slow Decay of Correlations.- 8 Modifications of d-Markov Gaussian Fields (Interpolation of Inverse Covariance).- 5. Expansions Around Ground States (Low-Temperature Expansions).- 1 Discrete Spin: Countable Number of Ground States.- 2 Continuous Spin: Unique Ground State.- 3 Continuous Spin: Two Ground States.- 6. Decay of Correlations.- 1 Hierarchy of the Properties of Decay of Correlations.- 2 An Analytic Method of Estimation of Semi-Invariants of Bounded Quasi-Local Functionals.- 3 A Combinatorial Method of Estimation of Semi-Invariants in the Case of Exponentially-Regular Cluster Expansion.- 4 Slow (power) Decay of Correlations.- 5 Low-Temperature Region.- 6 Scaling Limit of a Random Field.- 7. Supplementary Topics and Applications.- 1 Gibbs Quasistates.- 2 Uniqueness of Gibbs Fields.- 3 Compactness of Gibbs Modifications.- 4 Gauge Field with Gauge Group Z2.- 5 Markov Processes with Local Interaction.- 6 Ensemble of External Contours.- Concluding Remarks.- Bibliographic Comments.- References.

Singularities in the Critical Surface and Universality for Ising-Like Spin Systems

Abstract: It is shown that singularities appear in the shape of the critical surface of Ising-like spin systems for special interactions such as occur in the symmetric eight-vertex model. The nature of the singularity and the connection with breakdown of universality are given.

A scaling theory for the long-range to short-range crossover and an infrared duality*

Abstract: We study the second-order phase transition in the d-dimensional Ising model with long-range interactions decreasing as a power of the distance 1/r(d+s). For s below some known value s(*), the transition is described by a conformal field theory without a local stress tensor operator, with critical exponents varying continuously as functions of s. At s = s(*), the phase transition crosses over to the short-range universality class. While the location s(*) of this crossover has been known for 40 years, its physics has not been fully understood, the main difficulty being that the standard description of the long-range critical point is strongly coupled at the crossover. In this paper we propose another field-theoretic description which, on the contrary, is weakly coupled near the crossover. We use this description to clarify the nature of the crossover and make predictions about the critical exponents. That the same long-range critical point can be reached from two different UV descriptions provides a new example of infrared duality.