Nature of the spin-glass phase at experimental length scales

TL;DR

This study uses large-scale equilibrium simulations of 3D Ising spin glasses to connect experimental non-equilibrium results with theoretical models, confirming Replica Symmetry Breaking at relevant length scales.

Contribution

It demonstrates the applicability of equilibrium finite-size simulations to experimental non-equilibrium spin glasses and improves simulation methodologies for equilibration.

Findings

Non-equilibrium experiments on one hour match equilibrium L=110 lattices.

Replica Symmetry Breaking accurately describes the physics at relevant scales.

Established a time-length dictionary linking experiments and simulations.

Abstract

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.