The correlation functions of the Z-invariant Ising model are calculated explicitely using the Vertex Operators language developed by the Kyoto school.

This paper gives an introduction to the Random Field Ising Model (RFIM). Since its rst discussion in the paper by Imry and Ma 1] there has been great interest in this model, since Ising or Ising-like systems in random elds are a good representation of a large number of impure materials. These show features that can not be understood by studying ideal systems (i.e. Ising model). There are a lot ...

In other words, full conditional distribution of Xn depends of only on the neighbors Xn−1 and Xn+1. In the 2-D setting, assume that S = {1, 2, . . . , N} × {1, 2, . . . , N} is the set of N2 points, called sites. For a fixed site s define a neighborhood N(s). For example for the site (i, j) the neighborhood could be N((i, j)) = {(i− 1, j), (i + 1, j), (i, j − 1), (i, j + 1)}, where one may take...

The physics of phase transitions can be modeled by an arrangement of sites in a d-dimensional lattice known as the Ising model, in which each site is assigned either a positive or negative spin. In this paper, we will first provide an introduction to the Ising model. We will define the partition function of an Ising system, and present the problem of its computation. In 1993, Jerrum and Sinclai...

Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. T...