Exact mapping of a spin glass with correlated disorder to the pure Ising model

Abstract

We introduce an Ising spin-glass model with correlated disorder which continuously interpolates between the pure ferromagnetic Ising model and the Edwards-Anderson model with symmetric disorder. For this model, we prove that a Nishimori line (NL) can be defined, analogously to the Edwards-Anderson model, on which physical quantities can be expressed exactly in terms of those of the pure Ising model at a well-defined effective temperature on any lattice in any dimension. For example, the energy on the NL is equal to the energy of the pure Ising model at the effective temperature up to a constant and a trivial factor. More remarkably, the specific heat on the NL equals the energy, not the specific heat, of the pure Ising model at the effective temperature, again up to a constant and a trivial factor. Gauge-noninvariant quantities such as the magnetization and correlation functions are exactly equal to the corresponding quantities of the pure Ising model at the effective temperature. These exact relations imply that the leading critical behavior at that multicritical point for the disorder-correlated model is pure-Ising-like, in contrast to the conventional multicritical universality class of the standard Edwards-Anderson model. Our results motivate further investigations of the relatively unexplored topic of correlations in disorder in spin glasses and related problems.