Damage Spreading at the Corner Filling Transition in the two-dimensional Ising Model

TL;DR

This study investigates damage spreading in a 2D Ising model with corner geometry, revealing distinct propagation regimes at the filling transition temperature and highlighting the influence of geometry on damage dynamics.

Contribution

It provides the first detailed analysis of damage propagation at the corner filling transition in the 2D Ising model, identifying two distinct dynamic regimes and their relation to interface behavior.

Findings

Damage propagates along the interface with a power law at the filling transition.

The initial damage spreading exponent matches that of the wetting transition.

Damage later propagates into the bulk with a different, lower exponent.

Abstract

The propagation of damage on the square Ising lattice with a corner geometry is studied by means of Monte Carlo simulations. It is found that, just at $T=T_f (h)$ (critical temperature of the filling transition) the damage initially propagates along the interface of the competing domains, according to a power law given by $D(t) \propto t^{\eta}$. The value obtained for the dynamic exponent ($\eta^{*} = 0.89(1)$) is in agreement with that corresponding to the wetting transition in the slit geometry (Abraham Model) given by $\eta^{WT} = 0.91(1)$. However, for later times the propagation crosses to a new regime such as $\eta^{**} = 0.40 \pm 0.02$, which is due to the propagation of the damage into the bulk of the magnetic domains. This result can be understood due to the constraints imposed to the propagation of damage by the corner geometry of the system that cause healing at the corners where the interface is attached.