Nearest-neighbor frustrated random-bond model in<i>d=2</i>: Some exact results

Abstract

We study a d=2 Ising model where the veritcal bonds are fixed and ferromagnetic and the horizontal bonds can vary randomly in sign and in magnitude (within some limits) but are same within each now. The model therefore generalizes that of McCoy and Wu since it allows for the interesting case of frustration. We use the transfer matrix to map our problem to a collection of random field d=1 problems about which a lot is known. We find generally three transitions: a Griffiths transition, its dual version, and one with infinite correlation length and index \ensuremath{\nu}=1. In all cases the free energy has infinitely differentiable singularities. In addition there are some zero-temperature transitions.