Glassy Behaviour of Random Field on Bethe Lattice in an External Magnetic Field

Abstract

The magnetic random systems with a frustration in the exchange interactions between the spins exhibit a spin-glass phase at low temperature [1, 2]. The Sherrington-Kirkpatrick (SK) model with infinite-ranged interactions was suggested as a mean field model of spin-glasses [3]. Parisi found a stable solution using the replica-symmetry-breaking scheme [4]. The random field Ising model (RFIM) is one of the simplest models of disordered interacting systems. This RFIM describes the behavior of diluted antiferromagnets in strong magnetic fields [5]. In recent years, there have been many theoretical [6] and experimental indications [7]. The essential difficulties in breakdown the behaviour of the RFIM may be related to the existence of