Testing statics-dynamics equivalence at the spin-glass transition in three dimensions

TL;DR

This paper uses Monte Carlo simulations to verify the statics-dynamics equivalence in three-dimensional Ising spin glasses, achieving accurate critical behavior results by analyzing large coherence lengths.

Contribution

It demonstrates the application of statics-dynamics equivalence to study critical behavior in 3D spin glasses using large-scale simulations.

Findings

Excellent agreement with equilibrium computations

Clarification of the physical meaning of the dynamic exponent

Validation of the statics-dynamics correspondence at criticality

Abstract

The statics-dynamics correspondence in spin glasses relate non-equilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.