Mpemba Effect and Superuniversality across Orders of Magnetic Phase Transition

TL;DR

This study demonstrates that the Mpemba effect, where hotter systems cool faster than colder ones, also occurs in magnetic phase transitions, showing faster ferromagnetic ordering in hotter paramagnets across various models.

Contribution

The paper extends the Mpemba effect to magnetic phase transitions using Monte Carlo simulations, revealing its universality across different models and transition orders.

Findings

Hotter paramagnets order faster than colder ones.

The effect is consistent across models with varying interactions and dimensions.

A scaling relation links the effect to initial state correlations.

Abstract

The quicker freezing of hotter water, than a colder sample, when quenched to a common lower temperature, is referred to as the Mpemba effect (ME). While this counter-intuitive fact remains a surprize since long, efforts have begun to identify similar effect in other systems. Here we investigate the ME in a rather general context concerning magnetic phase transitions. From Monte Carlo simulations of model systems, viz., the $q$-state Potts model and the Ising model, with varying range of interaction and space dimension, we assert that hotter paramagnets undergo ferromagnetic ordering faster than the colder ones. The above conclusion we have arrived at following the analyses of the simulation results on decay of energy and growth in ordering following quenches from different starting temperatures, to fixed final temperatures below the Curie points. We have obtained a unique scaling picture, on the strength of the effect, with respect to the variation in spatial correlation in the initial states. These results are valid irrespective of the order of transition and relevant to the understanding of ME in other systems, including water.