A Field Theory for Finite Dimensional Site Disordered Spin Systems

TL;DR

This paper introduces a novel field theoretic approach for finite dimensional disordered spin systems with quenched randomness in the number of spins, revealing a spin glass phase with continuous replica symmetry breaking.

Contribution

It develops a new field theory using grand canonical disorder and applies the variational replica formalism to analyze phase behavior in disordered spin systems.

Findings

Identification of a spin glass phase with continuous replica symmetry breaking

Explicit analysis of a three-dimensional system exhibiting spin glass behavior

Suggestion that ferromagnetic transitions occur within the spin glass phase

Abstract

We present a new field theoretic approach for finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. We analyze this field theory using the variational replica formalism. For a variety of interactions we find a spin glass phase (with continuous replica symmetry breaking) and explicitly discuss a three dimensional system where this occurs. This approximation also suggests that any ferromagnetic transition occur within the spin glass phase.