Effects of geometry, boundary condition and dynamical rules on the magnetic relaxation of Ising ferromagnet

Ishita Tikader, Olivia Mallick, Muktish Acharyya

Published 2022-12-04Version 1

We have studied the magnetic relaxation behavior of a two-dimensional Ising ferromagnet by Monte Carlo simulation. Our primary goal is to investigate the effects of the system's geometry, boundary conditions, and dynamical rules on the relaxation behavior. The Glauber and Metropolis dynamical rules have been employed. The periodic and open boundary conditions are applied. The major findings are the dependence of relaxation (exponential) time ($\tau$) on the aspect ratio $R$ (length over breadth). In the limit of a small aspect ratio, the relaxation time is almost independent of the geometrical structure. However, a power law dependence ($\tau \sim R^{-s}$) has been observed for larger values of aspect ratios. The exponent ($s$) has been found to depend linearly ($s=aT+b$) on the system's temperature($T$). The transient behaviours of the spin-flip density have also been investigated for both surface and bulk/core. The size dependencies of spin-flip density significantly differ for the surface and for the bulk. Both the bulk/core and surface spin-flip density was found to follow the power law $f_d \sim L^{-\alpha}$ in the ferromagnetic regime.The faster relaxation was observed for open boundary condition for any kind (Metropolis/Glauber) of dynamical rule. Similarly, Metropolis algorithm yields faster relaxation for any kind (open/periodic) of boundary condition.