The Damage Spreading Method in Monte Carlo Simulations: A brief overview and applications to confined magnetic materials

M. LETICIA RUBIO PUZZO; EZEQUIEL V. ALBANO

Communications in Computational Physics

Global Science Press

Año: 2008 vol. 4 p. 207 - 230

1815-2406

The Damage Spreading (DS) method allows the investigation of the effect caused by tiny perturbations, in the initial conditions of physical systems, on their final stationary or equilibrium states. The damage (D(t)) is determined during the dynamic evolution of a physical system and measures the time dependence of the difference between a reference (unperturbed) configuration and an initially perturbed one.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 exhibit a transition between a state where the damage becomes healed (the frozen phase) and a 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 are actually true irreversible phase transitions themselves, and the issue of their universality class is also discussed.Subsequently, the attention is focused on the propagation of damage in magnetic systems placed in confined geometries. The influence of interfaces between magnetic domains of different orientation on the spreading of the perturbation is also discussed, showing that the presence of interfaces enhances the propagation of the damage. Furthermore, the critical transition between propagation and nonpropagation of the damage is discussed. The results analyzed indicate that, in some cases as in theAbraham´s Model and in the standard Ising magnet (Glauber dynamics), there is clear evidence showing that the DS transition and the critical transition of the physical system (in these cases the wetting and the ferromagnet-paramagnet transitions, respectively) occur at different critical points. However, in the case of the corner geometry, the critical points of both transitions-damage spreading and cornerfilling-coincide within error bars. It is found that, at criticality, the damage obeys a power-law behavior of the form D(t)=D0 t^n, where n is the damage spreading critical exponent. The evaluation of critical exponents allows the identification of three propagation regimes: i) inside the magnetic domains the propagation is slow n=0.40(2)), ii) the fast propagation is observed along the interface between domains n=0.90(2)), iii) the alternating propagation across interfaces and inside domains is consistent with an exponent lying between the previous cases, namely n=0.47(1). In all cases, the determined critical exponents suggest that the DS transition does not belong to the universality class of Directed Percolation, unlike many other systems exhibiting irreversible phase transitions. This result reflects the dramatic influence of interfaces on the propagation of perturbations in magnetic systems.