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

TL;DR

This study uses Monte Carlo simulations to analyze how geometry, boundary conditions, and dynamical rules influence the magnetic relaxation in a 2D Ising ferromagnet, revealing exponential relaxation, aspect ratio effects, and boundary-dependent relaxation times.

Contribution

It provides new insights into the effects of system geometry, boundary conditions, and dynamical rules on magnetic relaxation behavior in 2D Ising models, including dependencies of relaxation time and spin-flip densities.

Findings

Relaxation time depends exponentially on aspect ratio R.

Power law relation between relaxation time and R for large R.

Open boundary conditions and Metropolis dynamics lead to faster relaxation.

Abstract

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 (area preserving) , boundary conditions, and dynamical rules on the relaxation behavior. The Glauber and Metropolis dynamical rules have been employed. The systems with periodic and open boundary conditions are studied. The major findings are the exponential relaxation and the dependence of relaxation time ($\tau$) on the aspect ratio $R$ (length over breadth having fixed area). A power law dependence ($\tau \sim R^{-s}$) has been observed for larger values of aspect ratio ($R$). 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 been investigated for both surface and bulk/core. The size dependencies of saturated spin-flip density significantly differ for the surface and the bulk/core. Both the saturated bulk/core and saturated surface spin-flip density was found to follow the logarithmic dependence $f_d = a + b~log(L)$ with the system size. The faster relaxation was observed for open boundary condition with any kind (Metropolis/Glauber) of dynamical rule. Similarly, Metropolis algorithm yields faster relaxation for any kind (open/periodic) of boundary condition.