Two-dimensional Ising model with annealed random fields

Abstract

We investigate the influence of annealed random fields on the phase diagram of the ferromagnetic Ising model on the square lattice. We find that the gaussian random field makes the ferromagnetic ground state unstable and we have a super-antiferromagnetic state at low temperatures. For the binary random field, in which the random field takes + h with probability p and - h with probability 1 - p, there is a critical field h c, and the ferromagnetic ground state is stable for h < h c but unstable for h 62 h c. When the ferromagnetic ground state is unstable, we have a re-entrant phase transition.