Ordering in the infinite-ranged Ising spin glass - Exact solutions for small samples

Abstract

A new order parameter q(2) for the infinite-ranged Ising spin glass model is introduced. q(2) can be defined without specifying any symmetry breaking field, and is a direct measure of the effect of frustration on the internal energy below the spin glass transition temperature, T sg. An exact evaluation of q(2)(T) for small systems (with up to 20 spins) establishes the existence of Edwards-Anderson ordering, and sheds light on several of the controversies which surround this model.