Persistence in Ferromagnetic Ordering: Dependence upon initial configuration

TL;DR

This study investigates how the initial temperature affects the ordering dynamics in ferromagnets modeled by the Ising model, revealing different persistence behaviors and a potential new universality class at critical initial conditions.

Contribution

It introduces a detailed analysis of the impact of initial temperature on persistence and domain growth, identifying a possible new universality class at the critical initial temperature.

Findings

Persistence exponents vary with initial temperature and dimension.

A new universality class emerges at initial temperature equal to critical temperature.

Domain growth is largely unaffected by initial temperature.

Abstract

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures ($T_f$) below the critical one ($T_{c}$), from different initial temperatures $T_{i} \geq T_{c}$. In long time limit, for $T_{i} > T_{c}$, the persistence probability exhibits power-law decay with exponents $\theta \simeq 0.22$ and $\simeq 0.18$ in $d=2$ and $3$, respectively. For finite $T_i$, the early time behavior is a different power-law whose life-time diverges and exponent decreases as $T_{i} \rightarrow T_{c}$. The crossover length between the two steps diverges as the equilibrium correlation length. $T_i=T_c$ is expected to provide a {\it{new universality class}} for which we obtain $\theta \simeq 0.035$ in $d=2$ and $\simeq 0.10$ in $d=3$. The time dependence of the average domain size $\ell$, however, is observed to be rather insensitive to the choice of $T_i$.