Replica field theory and renormalization group for the Ising spin glass in an external magnetic field

TL;DR

This paper applies replica symmetric cubic field theory and renormalization group analysis to study the critical behavior of short-range Ising spin glasses in a magnetic field near six dimensions, revealing a new fixed point and unusual mode behavior.

Contribution

It introduces a novel fixed point in the renormalization group analysis for Ising spin glasses in a magnetic field, expanding understanding of their critical behavior.

Findings

Discovery of a new fixed point governing critical behavior in a magnetic field.

Divergence of spin glass susceptibility at criticality.

Unusual jump in the anomalous mode at the transition.

Abstract

We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero magnetic field fixed-point, from the application of the renormalization group. In the spin glass limit, n going to 0, this fixed-point governs the critical behaviour of a class of systems characterised by a single cubic interaction parameter. For this universality class, the spin glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, the so-called anomalous one, however, behaves unusually, having a jump at criticality. The physical consequences of this unusual behaviour are discussed, and a comparison with the conventional de Almeida-Thouless scenario presented.