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

Significance The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, etc.) is a sluggish dynamics at low temperatures. Indeed, their dynamics are 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. This relation is made quantitative via a statics-dynamics dictionary, established for spin glasses. In our dictionary, the aging response to a magnetic field is related to the spin-glass order parameter as obtained on samples small enough to equilibrate. We remark that all of the observables we consider can be measured with current experimental methods. We have performed a very accurate computation of the nonequilibrium fluctuation–dissipation ratio for the 3D 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. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.