Ising-Glauber dynamics of a frustrated spin system in a hexagonal-triangular configuration

Abstract

We investigate the evolution of the magnetization probability and the average magnetization of a frustrated antiferromagnet in a hexagonal-triangular geometry using Ising-Glauber dynamics. We derive the transition probability matrix and calculate the evolution of the magnetization probability for various initial conditions in three main regimes: i.) when the exchange coupling J dominates the thermal energy kT, ii.) When the coupling is comparable to the thermal energy and iii.) When the thermal energy dominates the exchange coupling. We found that higher magnetizations acquire non-zero probabilities when the thermal energy becomes non-negligible compared to J, even after many time iterations. Systems starting from different initial conditions converge to the same steady-state magnetization values.