A Minimal Mechanism for the Phase Transition-Driven Mpemba Effect in Systems with a Single Order Parameter.

The Mpemba effect, where a hotter system can enter a cold phase faster than a cooler one, remains a counterintuitive phenomenon whose origins are still being unraveled. In this work, we propose and demonstrate a simple and general mechanism for the genuine, phase transition-driven Mpemba effect. Our mechanism requires only a single order parameter to describe the system's state and operates within a standard Markovian framework, distinguishing it from previous models that necessitate multiple order parameters or non-Markovian dynamics. The core of the effect lies in the distinct relaxation pathways following a sudden quench: a system prepared at a higher initial temperature may be projected onto a region of the final free-energy landscape that requires it to cross fewer energy barriers to reach the stable low-temperature phase, whereas a system prepared at an intermediate temperature may be trapped in a metastable state, requiring the crossing of multiple barriers. We concretely illustrate this mechanism using the extended spin-1 Nagle-Kardar model, where an appropriate choice of parameters yields the requisite free-energy topography. Through extensive Monte Carlo simulations, we confirm that the initially hot system consistently reaches the final ferromagnetic phase in less time than its initially warm counterpart, thereby exhibiting a robust Mpemba effect. Our findings provide a minimal and clear explanation for how the initial state's position in order parameter space can dictate the kinetics of a first-order phase transition, leading to this anomalous acceleration of cooling.