Exact solution of a 2d random Ising model

TL;DR

This paper provides an exact solution for a two-dimensional layered random Ising model with specific coupling configurations, revealing phase transition behaviors and glassy properties under different disorder correlations.

Contribution

It introduces an exact solution for a 2D layered random Ising model in the limit of infinite K, analyzing phase transitions and glassy phases for correlated and independent disorder.

Findings

No phase transition with independent disorder

Existence of a low-temperature glassy phase with correlated disorder

Exact analytical solution in the infinite K limit

Abstract

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 limit case of infinite K for any distribution of the horizontal couplings. The model which corresponds to this limit can be seen as an ordinary Ising system where the spins of some rows, chosen at random, are frozen in an antiferromagnetic order. No phase transition is found if the horizontal couplings are independent random variables while for correlated disorder one finds a low temperature phase with some glassy properties.