Behavior of Ising Spin Glasses in a Magnetic Field

TL;DR

This paper investigates the existence of a spin-glass phase in a magnetic field through Monte Carlo simulations, finding evidence for the instability line in mean-field models but not in short-range three-dimensional models.

Contribution

It introduces a simulation method crossing the instability line and compares results between mean-field and short-range models, revealing differences in phase behavior.

Findings

Instability line confirmed in Bethe lattice model.

No instability line found in 3D short-range model.

Method effectively tests phase transition lines.

Abstract

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field--temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.