The Arena of Conformal Models

2020 ◽  
pp. 518-542
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Statistical Models ◽  
Statistical Physics ◽  
The Self ◽  
Minimal Models ◽  
Lee Model ◽  
Geometric Type ◽  
Structure Constants ◽  
Self Avoiding Walks ◽  
Conformal Models

Chapter 14 discusses how the identification of a class of universality is one of the central questions needing an answer for those in the field of statistical physics. This chapter discusses in detail the class of universality of several models, and provides examples that include the Ising model, the tricritical Ising model and its structure constants, the Yang–Lee model and the 3-state Potts model. This chapter also covers the study of the statistical models of geometric type (as, for instance, those that describe the self-avoiding walks) and their formulation in terms of conformal minimal models, including conformal models with O(n) symmetry.

scholarly journals Concepts on statistical physics - fluctuations in equilibrium

2015 ◽  
Vol 4 (1) ◽  
pp. 1-27
Author(s):  
L´eon Brenig
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Ising Model ◽  
Critical Exponents ◽  
Statistical Models ◽  
Statistical Physics ◽  
Lattice Gas ◽  
Simple Fluids ◽  
Large Numbers ◽  
Starting Point

This essay corresponds to the content of three lectures about statistical physics delivered to the audience of the 2014 section of the R. A. Salmeron School of Physics, at the UnB. Our starting point was very simple statistical models (lattice gas, spin-1/2 ferromagnet), used as illustrations of the competencies and methods in statistical physics. Thus we introduce the Gibbs ensembles, defining a connection with thermodynamics and discussing the role played by fluctuations and large numbers. We present phenomenological aspects of phase transitions and critical phenomena in simple fluids and in uniaxial ferromagnets, emphasizing the universal character of the critical exponents. We describe the phenomenological van der Waals and Curie-Weiss theories and the Landau expansion, which are present-day relevant methods, despite the fact that such theories give rise to critical exponents in disagreement with experiments. We present then the paradigmatic Ising model, which points us to a way to overcome the phenomenological results. A brief presentation of the scale phenomenological methods and the contemporaneous renormalization group are considered at the end of these lectures.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

Specific Heat of Square Spin Ice in Finite Point Ising-Like Dipoles Model

2015 ◽  
Vol 245 ◽  
pp. 23-27 ◽  
Author(s):  
Yuriy Shevchenko ◽  
Vitalii Kapitan ◽  
Konstantin V. Nefedev
Keyword(s):  
Finite Number ◽  
Statistical Models ◽  
Statistical Physics ◽  
Calculation Methods ◽  
Magnetostatic Interaction ◽  
Finite Point ◽  
Magnetic Dipoles ◽  
Higher Temperature ◽  
Gibbs Formalism ◽  
Number Of Particles

In the model of finite number (up to 24) of point Ising-like magnetic dipoles with magnetostatic interaction on square 2D lattice within the framework of statistical physics, with using Gibbs formalism and by the means of Metropolis algorithm the heating dependence of temperature has been evaluated. The temperature dependence of the heat capacity on finite number of point dipoles has the finite value of maximum. Together with increase of the system in size the heating peak grows and moves to the area with higher temperature. The obtained results are useful in experimental verification of statistical models, as well as in development and testing of approximate calculation methods of systems with great number of particles.

Exact S-Matrices

2020 ◽  
pp. 676-743
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Quantum Group ◽  
Scattering Theory ◽  
Integrable Model ◽  
Group Symmetry ◽  
Fusion Rules ◽  
Lee Model ◽  
Sine Gordon Model ◽  
Multiple Poles

The Ising model in a magnetic field is one of the most beautiful examples of an integrable model. This chapter presents its exact S-matrix and the exact spectrum of its excitations, which consist of eight particles of different masses. Similarly, it discusses the exact scattering theory behind the thermal deformation of the tricritical Ising model and the unusual features of the exact S-matrix of the non-unitary Yang–Lee model. Other examples are provided by O(n) invariant models, including the important Sine–Gordon model. It also discusses multiple poles, magnetic deformation, the E 8 Toda theory, bootstrap fusion rules, non-relativistic limits and quantum group symmetry of the Sine–Gordon model.

Ground States, Energy Landscape, and Low-Temperature Dynamics of ± J Spin Glasses

2005 ◽  
Author(s):  
Sigismund Kobe ◽  
Jarek Krawczyk
Keyword(s):  
Ising Model ◽  
Spin Glass ◽  
Spin Glasses ◽  
Statistical Physics ◽  
Energy Landscape ◽  
Point Of View ◽  
Model Systems ◽  
Spin Glass Model ◽  
Glass Model ◽  
Physics Literature

The previous three chapters have focused on the analysis of computational problems using methods from statistical physics. This chapter largely takes the reverse approach. We turn to a problem from the physics literature, the spin glass, and use the branch-and-bound method from combinatorial optimization to analyze its energy landscape. The spin glass model is a prototype that combines questions of computational complexity from the mathematical point of view and of glassy behavior from the physical one. In general, the problem of finding the ground state, or minimal energy configuration, of such model systems belongs to the class of NP-hard tasks. The spin glass is defined using the language of the Ising model, the fundamental description of magnetism at the level of statistical mechanics. The Ising model contains a set of n spins, or binary variables si, each of which can take on the value up (si = 1) or down (si= 1).

Percolation of a random network by statistical physics method

2019 ◽  
Vol 30 (02n03) ◽  
pp. 1950009
Author(s):  
Hai Lin ◽  
Jingcheng Wang
Keyword(s):  
Ising Model ◽  
Cluster Model ◽  
Statistical Physics ◽  
Random Network ◽  
Critical Phenomenon ◽  
Analytical Framework ◽  
Critical Value ◽  
Giant Component ◽  
Random Cluster Model ◽  
Random Cluster

In this paper, we develop an analytical framework and analyze the percolation properties of a random network by introducing statistical physics method. To adequately apply the statistical physics method on the research of a random network, we establish an exact mapping relation between a random network and Ising model. Based on the mapping relation and random cluster model (RCM), we obtain the partition function of the random network and use it to compute the size of the giant component and the critical value of the present probability. We extend this approach to investigate the size of remaining giant component and the critical phenomenon in the random network which is under a certain random attack. Numerical simulations show that our approach is accurate and effective.

ON THE SELF-AVOIDING WALKS ON DISORDERED LATTICES

1986 ◽  
pp. 115-118
Author(s):  
S. MILOŠEVIĆ ◽  
A. CHERNOUTSAN
Keyword(s):  
The Self ◽  
Self Avoiding Walks
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