4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

TL;DR

This study uses numerical simulations to demonstrate that 4D spin glasses in a magnetic field exhibit a phase transition similar to mean field theory, with evidence of replica symmetry breaking and compatible critical exponents.

Contribution

It provides numerical evidence that 4D Edwards Anderson spin glasses in a magnetic field have a mean field like phase transition with replica symmetry breaking.

Findings

Demonstrates a phase transition in 4D spin glasses in a magnetic field.

Shows the dynamic overlap converges to a value indicating replica symmetry breaking.

Critical exponents align with mean field predictions.

Abstract

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.