Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point

TL;DR

This paper analyzes the asymptotic behavior of physical observables in the 6-ε dimensional Ising spin glass near the critical fixed point, using an effective field theory and renormalization group methods.

Contribution

It introduces a perturbative effective field theory framework to study the critical behavior of spin glasses under small magnetic fields near the zero-field transition.

Findings

Identifies the scaling functions for order parameter and masses.

Defines the Almeida-Thouless surface via the replicon mass zero.

Provides insights into the critical fixed point structure.

Abstract

The asymptotical behavior of physical quantities, like the order parameter, the replicon and longitudinal masses, is studied around the zero-field spin glass transition point when a small external magnetic field is applied. An effective field theory to model this asymptotics contains a small perturbation in its Lagrangian which breaks the zero-field symmetry. A first order renormalization group supplemented by perturbational results provides the scaling functions. The perturbative zero of the scaling function for the replicon mass defines a generic Almeida-Thouless surface stemming from the zero-field fixed point.