Spin glass transition in a magnetic field: a renormalization group study

TL;DR

This paper investigates the critical behavior of short-range Ising spin glasses in magnetic fields using renormalization group techniques, revealing the instability of the zero-field fixed point and the absence of a stable fixed point for the de Almeida-Thouless transition.

Contribution

It introduces a comprehensive replica symmetric field theory with multiple modes and couplings, analyzing the spin glass transition in both zero and non-zero fields within a unified framework.

Findings

A stable fixed point exists for zero-field transition.

The fixed point becomes unstable with a magnetic field.

No stable fixed point is found for the AT transition in finite fields.

Abstract

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.