Strong Mpemba Effect Through a Reentrant Phase Transition

Abstract

We investigate temperature quenches across the reentrant phase transition of the antiferromagnetic Ising model in a magnetic field and show that it provides a natural mechanism for strong direct and inverse Mpemba effects. For quenches terminating in the paramagnetic phase, the slowest relaxation mode is purely staggered. Initial states in the paramagnetic phase therefore have exactly zero overlap with this mode and exhibit a strong Mpemba effect, whereas antiferromagnetic initial states excite it and develop a slow-relaxation tail. Moreover, reentrance makes the equilibrium staggered magnetization nonmonotonic, producing conventional direct and inverse Mpemba effects when both initial states lie in the antiferromagnetic phase and the quench terminates in the paramagnetic phase. By varying the lattice coordination number, we show that this mechanism disappears in the absence of reentrance. Our results provide the first demonstration of (strong) Mpemba effects in the antiferromagnetic Ising model within the pair approximation and establish a direct link between anomalous relaxation and equilibrium phase behavior.