Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations

TL;DR

This paper investigates the phase transition in the 3D Ising spin glass by analyzing out-of-equilibrium simulations to determine the Edwards-Anderson order parameter and its scaling behavior.

Contribution

It introduces a method to compute the Edwards-Anderson order parameter from out-of-equilibrium data and compares it with equilibrium results, providing new insights into the phase transition.

Findings

The out-of-equilibrium order parameter matches the critical law observed in experiments.

The order parameter's dependence on lattice size is characterized.

Scaling of fluctuation-dissipation relations is analyzed over large times.

Abstract

Using the decay of the out equilibrium spin-spin correlation function we compute the equilibrium Edward-Anderson order parameter in the three dimensional binary Ising spin glass in the spin glass phase. We have checked that the Edward-Anderson order parameter computed from out of equilibrium numerical simulations follows with good precision the critical law as determined in experiments and in numerical studies at equilibrium. We have also studied the dependence of the order parameter with the lattice size. Finally we present a large time study of the scaling of the off-equilibrium fluctuation-dissipation relations.