Transient behavior of damage spreading in the two-dimensional Blume-Capel ferromagnet

TL;DR

This study investigates how damage spreads and heals over time in a two-dimensional spin-1 Blume-Capel model, revealing exponential decay behavior influenced by various parameters and differences between Monte Carlo dynamics methods.

Contribution

It provides new insights into the transient damage behavior in the Blume-Capel model, highlighting the dependence on Hamiltonian parameters and comparing different simulation dynamics.

Findings

Damage decays exponentially in certain regimes.

Decay rate depends linearly on model parameters.

Glauber dynamics shows slower damage decay.

Abstract

We study the transient behavior of damage propagation in the two-dimensional spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field--temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.