Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model

TL;DR

This study uses Monte Carlo simulations of the Ising model to demonstrate a counter-intuitive Mpemba effect where hotter ferromagnetic systems relax faster to equilibrium than cooler ones, highlighting the role of critical fluctuations.

Contribution

First simulation-based evidence of the Mpemba effect in ferromagnets, showing faster relaxation from higher initial temperatures without frustration or metastability.

Findings

Hotter initial states relax faster to equilibrium.

The Mpemba effect occurs without frustration or metastability.

Critical fluctuations influence the relaxation dynamics.

Abstract

For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing fact, referred to as the Mpemba effect (ME), during ordering in ferromagnets. By performing Monte Carlo simulations of a generic model, we have obtained results on relaxation of systems that are quenched to sub-critical state points from various temperatures above the critical point. For a fixed final temperature, a system with higher starting temperature equilibrates faster than the one prepared at a lower temperature, implying the presence of ME. The observation is extremely counter-intuitive, particularly because of the fact that the model has no in-built frustration or metastability that typically is thought to provide ME. Via the calculations of nonequilibrium properties concerning structure and energy, we quantify the role of critical fluctuations behind this fundamental as well as technologically relevant observation.