On the critical temperature of the two-dimensional Ising spin glass models

Abstract

The critical temperature for a quenched Ising model on the square lattice, with vertical random interactions, is found exactly. The detailed phase diagram is obtained for the bond-dilute model and for the model with mixed ferro- and antiferromagnetic delta distribution of the bonds. For the class of the models with symmetric distribution of the bonds (P(J)=P(-J)) it is shown that the critical temperature is always equal to zero. An immediate consequence of this is the theorem about the absence of the second-order phase transitions for the square, fully random, quenched Ising model with symmetric distribution of the bonds.