2D ISING MODEL WITH A DEFECT LINE

Vitrification in a 2D Ising model with mobile bonds

A bond-disordered two-dimensional Ising model is used to simulate Kauzmann’s mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to nearest neighbors at the same rate as the spins flip. For slow cooling, the theoretical minimum energy configuration is approached, characterized by an amorpho...

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 ...

Institute for Mathematical Physics on Local Behaviour of the Phase Separation Line in the 2d Ising Model on Local Behaviour of the Phase Separation Line in the 2d Ising Model

The aim of this note is to discuss statistical properties of the phase separation line in the 2D Ising model. The aymptotical properties of the random process corresponding to the uctuations of the phase boundary in the direction orthogonal to its orientation are described on the level of the functional central limit theorem. The limiting Gaussian measure corresponds to a scaled Brownian bridge...

Bethe-peierls Approximation for the 2d Random Ising Model

The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls approximations, using the replica method.