Exact solution of a 2d random Ising model

Details Exact solution of a 2d random Ising model Exact solution of a 2d random Ising model

1997-05-16

arxiv.org/abs/cond-mat/9705161v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, Plain TeX, 3 ps figures, submitted to Europhys. Lett

Scientific paper

10.1103/PhysRevE.56.R2339

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.

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