A Model for Damage Spreading with Damage Healing: Monte Carlo Study of the two Dimensional Ising Ferromagnet

TL;DR

This study introduces a damage spreading model with healing for the 2D Ising ferromagnet, revealing a critical damage spreading curve dependent on temperature and belonging to the directed percolation universality class.

Contribution

The paper proposes a new damage healing model for the Ising system and characterizes its phase diagram and critical behavior through Monte Carlo simulations.

Findings

Existence of a critical damage spreading curve depending on temperature.

Critical point $p_c$ varies with temperature, defining a phase boundary.

Damage remains active within a phase with stationary damage linearly dependent on parameters.

Abstract

An Ising model for damage spreading with a probability of damage healing ($q = 1 - p$) is proposed and studied by means of Monte Carlo simulations. In the limit $p \to 1$ the new model is mapped to the standard Ising model. It is found that, for temperatures above the Onsager critical temperature ($T_{C}$), there exist a no trivial finite value of $p$ that sets the critical point ($p_{c}$) for the onset of damage spreading. It is found that $p_{c}$ depends on $T$, defining a critical curve at the border between damage spreading and damage healing. Transitions along such curve are found to belong to the universality class of directed percolation. The phase diagram of the model is also evaluated showing that for large $T$ one has $p_{c} \propto (T- T_{C})^{\alpha}$, with $\alpha = 1$. Within the phase where the damage remains active, the stationary value of the damage depends lineally on both $p - p_{c}$ and $T - T_{C} $.