The de Almeida-Thouless line in vector spin glasses

TL;DR

This paper investigates the stability of the replica symmetric solution in vector spin glasses with multiple components under random magnetic fields, deriving the AT line location for any number of components and confirming results through simulations.

Contribution

It extends the understanding of the Almeida-Thouless line to vector spin glasses with arbitrary components, providing analytical calculations and numerical verification.

Findings

Derived the AT line for vector spin glasses with arbitrary m.

Confirmed theoretical predictions with numerical simulations for m=3.

Established the stability boundary for replica symmetry in vector spin glasses.

Abstract

We consider the infinite-range spin glass in which the spins have m > 1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is an Almeida Thouless (AT) line below which the "replica symmetric" solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m, and verify our results by numerical simulations for m = 3$.