The Mpemba effect in spin glasses is a persistent memory effect

Significance The Mpemba effect, wherein an initially hotter system relaxes faster when quenched to lower temperatures than an initially cooler system, has attracted much attention. Paradoxically, its very existence is a hot topic. Using massive numerical simulations, we show unambiguously that the Mpemba effect is present in the archetypical model system for complex behavior, spin glasses. We find that the Mpemba effect in spin glasses is due to the aging dynamics of the internal energy, as controlled by the nonequilibrium spin-glass coherence length. Interestingly, the effect is not present when the system remains all of the time in the paramagnetic phase. Therefore, the Mpemba effect suggests itself as an effective probe for a glass transition, potentially useful for other glass-forming systems. The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom-built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a nonequilibrium process, governed by the coherence length ξ of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and ξ that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.