Disappearance of the de Almeida-Thouless line in six dimensions

TL;DR

This paper demonstrates that the Almeida-Thouless line disappears in Ising spin glasses as the dimension approaches six, indicating a fundamental change in the system's behavior near this critical dimension.

Contribution

The study provides a theoretical proof that the Almeida-Thouless line vanishes at six dimensions and extends this result to long-range one-dimensional models, highlighting a key transition in spin glass physics.

Findings

Almeida-Thouless line disappears at d=6

Replica symmetry breaking ceases at d=6

Results applicable to long-range 1D spin glasses

Abstract

We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.