Ising spin glass transition in magnetic field out of mean-field

TL;DR

This paper investigates the existence of a spin-glass transition in a magnetic field within a long-range one-dimensional Ising model, challenging mean-field predictions and exploring lower-dimensional behaviors.

Contribution

It provides evidence for a spin-glass transition in magnetic field in systems below the upper critical dimension, extending understanding beyond mean-field theory.

Findings

Evidence of spin-glass transition in magnetic field below upper critical dimension

Long-range model simulates varying effective dimensions

Transition persists outside mean-field limit

Abstract

The spin-glass transition in external magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Evidence for a spin-glass transition in magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field.