Evolution of the magnetization probability of a frustrated antiferromagnet in a hexagonal-triangular lattice in discrete Glauber dynamics

Abstract

We investigate the evolution of the magnetization probability of a frustrated antiferromagnet in a hexagonal-triangular lattice in discrete time Glauber dynamics. This is done by taking the Ising Hamiltonian H = J Σ_(ij) S_i^z  S_i^z with positive coupling J as a model for the antiferro- magnet. We derive the single-time-step transition probability matrix and calculate the evolution of the magnetization probability for various initial conditions. We then investigate three main regimes: i.) x ≡ J/kT → ∞, ii.) x = 1 and iii.) x = 0.1, where kT is the thermal energy. We found that in the first regime, the magnetization probability strongly fluctuates between two values 1 and 0 for magnetizations M = ±1 with the rest of the magnetization probabilities for higher magnetizations |M| > 1 rapidly dropping to zero. When the thermal energy becomes non-negligible compared to J, the higher magnetizations acquire non-zero probabilities even after many time iterations.