Another solution of 2D Ising model

The solution of the 2D Ising model

Exact Solution of a 2d Random Ising Model

The model considered is a d = 2 layered random Ising system on a square lattice with nearest neighbours interaction. It is assumed that all the vertical couplings are equal and take the positive value J while the horizontal couplings are quenched random variables which are equal in the same row but can take the two possible values J and J −K in different rows. The exact solution is obtained in ...

The critical equation of state of the 2D Ising model

We compute the 2n-point coupling constants in the high-temperature phase of the 2d Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of th...

Macroscopic Description of Phase Separation in the 2D Ising Model

We review recent results about the macroscopic description of phase separation in the 2D Ising model, with special emphasis on boundary effects and related surface phase transitions. In particular, after having recalled some facts about the wetting transition, we describe two situations in which this transition has major consequences at the macroscopic scale. We also briefly describe a more gen...

Monte Carlo Simulation of the 2D Ising model

Monte Carlo methods are a powerful tool to solve problems numerically which are di cult to be handled analytically. Nevertheless, these methods are applied to one of the best studied models in statistical physics in the following: The Ising model, which was invented by Wilhelm Lenz and investigated by his student Ernst Ising in the 1920ies. In particular, the two-dimensional case with interacti...