A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

TL;DR

This paper establishes a quantitative link between non-equilibrium measurements and the low-temperature equilibrium phase of spin glasses, enabling experimental exploration of their properties without extrapolation.

Contribution

It introduces a statics-dynamics equivalence via the fluctuation-dissipation ratio, connecting measurable non-equilibrium quantities to the spin-glass phase.

Findings

Computed the non-equilibrium fluctuation-dissipation ratio for 3D Edwards-Anderson spin glass.

Compared the ratio with equilibrium spin overlap distributions.

Provided a practical framework for experimental investigation of spin-glass phases.

Abstract

The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is never reached in macroscopic samples: in analogy with living beings, glasses are said to age. Here, we show how to relate experimentally relevant quantities with the experimentally unreachable low-temperature equilibrium phase. We have performed a very accurate computation of the non-equilibrium fluctuation-dissipation ratio for the three-dimensional Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting quantitative statics-dynamics dictionary, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes.