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.