Site Disordered Spin Systems in the Gaussian Variational Approximation

TL;DR

This paper develops a replica field theory for finite-dimensional disordered spin systems with a novel grand canonical disorder approach, using Gaussian variational methods to predict spin glass phases and analyze symmetry breaking.

Contribution

It introduces a new theoretical framework for disordered spin systems with random system size and applies Gaussian variational approximation to analyze phase transitions.

Findings

Predicts a spin glass phase regardless of interaction form

Identifies diverging correlator at the spin glass transition

Discusses limitations of the approximation in ferromagnetic ordering

Abstract

We define a replica field theory describing 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. A general analysis of this field theory is made using the Gaussian variational or Hartree Fock method, and illustrated with several specific examples. Irrespective of the form of interaction between the spins this approximation predicts a spin glass phase. We discuss the replica symmetric phase at length, explicitly identifying the correlator that diverges at the spin glass transition. We also discuss the form of continuous replica symmetry breaking found just below the transition. Finally we show how an analysis of ferromagnetic ordering indicates a breakdown of the approximation.