Damage Spreading During Domain Growth

TL;DR

This paper investigates damage spreading during domain growth in two-dimensional systems undergoing first order phase transitions, revealing model-dependent growth laws and unexpected differences between dynamics types.

Contribution

It provides an exact solution for damage growth in the Ohta-Jasnow-Kawasaki model and compares it with simulation results for different dynamics, highlighting new insights into damage spreading behavior.

Findings

Exact damage growth law $D \\sim t^{d/4}$ in the Ohta-Jasnow-Kawasaki model

Power-law damage growth with exponent ~0.36 in Ginzburg-Landau and Ising models

Damage growth with exponent ~1 under Metropolis dynamics

Abstract

We study damage spreading in models of two-dimensional systems undergoing first order phase transitions. We consider several models from the same non-conserved order parameter universality class, and find unexpected differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model yields the damage growth law $D \sim t^{\phi}$, where $\phi = t^{d/4}$ in $d$ dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising simulations in $d= 2$ using heat-bath dynamics show power-law growth, but with an exponent of approximately $0.36$, independent of the system sizes studied. In marked contrast, Metropolis dynamics shows damage growing via $\phi \sim 1$, although the damage difference grows as $t^{0.4}$. PACS: 64.60.-i, 05.50.+q