Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions

TL;DR

This paper investigates the phase boundary in high-dimensional spin glasses, revealing a multicritical point on the de Almeida-Thouless line near six dimensions, with implications for critical behavior and perturbation theory validity.

Contribution

It identifies and analyzes a multicritical point on the AT line in dimensions just above six, showing how critical exponents and RG flows behave near this point.

Findings

Existence of a multicritical point on the AT line for d>6

Critical exponents at the MCP calculated to first order in ε=d-6

Perturbation theory breaks down at high fields near six dimensions

Abstract

The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature $T$ and magnetic field $h$ plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that when the dimension $d$ of space is just above $6$ there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime where the RG flows run away to infinite coupling strength; as $d$ approaches $6$ from above, the location of the MCP approaches the zero-field critical point exponentially in $1/(d-6)$. Thus on the AT line perturbation theory for the critical properties breaks down at sufficiently large magnetic field even above $6$ dimensions, as well as for all non-zero fields when $d\leq 6$ as was known previously. We calculate the exponents at the MCP to first order in $\varepsilon=d-6>0$. The fate of the MCP as $d$ increases from just above 6 to infinity is not known.