Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model

TL;DR

This study investigates how thermal fluctuations influence the interface geometry during phase ordering in the quenched Ising model, revealing that interface roughness affects scaling behavior and introduces crossover phenomena.

Contribution

It demonstrates the impact of interface roughening on phase-ordering kinetics and identifies a crossover from flat to curved interfaces depending on quench temperature.

Findings

Growth exponent z=2 remains unaffected by temperature.

Interface geometry varies with quench temperature, affecting scaling.

Roughening length causes significant corrections to scaling in 2D.

Abstract

We study the role of the quench temperature $T_f$ in the phase-ordering kinetics of the Ising model with single spin flip in $d=2,3$. Equilibrium interfaces are flat at $T_f=0$, whereas at $T_f>0$ they are curved and rough (above the roughening temperature in $d=3$). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent $z=2$ of the size of domains $L(t)\sim t^{1/z}$ is unaffected by $T_f$, other exponents related to the interface geometry take different values at $T_f=0$ or $T_f>0$. For $T_f>0$ a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at $T_f=0$, to the asymptotic regime with curved interfaces characteristic of $T_f>0$. Furthermore, it is shown that the roughening length, although sub-dominant with respect to $L(t)$, produces appreciable correction to scaling up to very long times in $d=2$.