The Damage Spreading Method in Monte Carlo Simulations: A Brief Overview and Applications to Confined Magnetic Materials (Communications in Computational Physics, 2018)
The Damage Spreading (DS) method allows the investigation of the effectcaused by tiny perturbations, in the initial conditions of physical systems, on theirfinal stationary or equilibrium states. The damage (D(t)) is determined during thedynamic evolution of a physical system and measures the time dependence of thedifference between a reference (unperturbed) configuration and an initially perturbedone. In this paper we first give a brief overview of Monte Carlo simulation results obtained by applying the DS method. Different model systems under study often exhibita transition between a state where the damage becomes healed (the frozen phase) anda regime where the damage spreads arriving at a finite (stationary) value (the damaged phase), when a control parameter is finely tuned. These kinds of transitions areactually true irreversible phase transitions themselves, and the issue of their universality class is also discussed. Subsequently, the attention is focused on the propagationof damage in magnetic systems placed in confined geometries. The influence of interfaces between magnetic domains of different orientation on the spreading of theperturbation is also discussed, showing that the presence of interfaces enhances thepropagation of the damage. Furthermore, the critical transition between propagationand nonpropagation of the damage is discussed. In all cases, the determined criticalexponents suggest that the DS transition does not belong to the universality class ofDirected Percolation, unlike many other systems exhibiting irreversible phase transitions. This result reflects the dramatic influence of interfaces on the propagation ofperturbations in magnetic systems.