The stochastic extraction of critical temperature in uniaxial anisotropic magnetic films: A finite size scaling analysis on harmonic order parameters

Abstract

In this work, the critical temperature of Ising ferromagnetic and anti-ferromagnetic systems in 2 dimensions was extracted via finite-size-scaling analysis on the order parameter calculated from the discrete Fourier transformation. Spin patterns under the effect of thermal fluctuation were generated using Monte Carlo simulation. The discrete Fourier transformation was used to transform spin patterns from spatial domain to wave vector domain, where the order parameter was calculated from this Fourier-harmonics. From the result, it was found that TC= 2.2684 ±0.0006J/kBfor ferromagnetic system and TC= 2.2689 ±0.0003J/kBfor anti-ferromagnetic system which match well with the exact theoretical value TC≈2.269 J/kB. As can be seen, the critical temperatures of both systems match well with the exact theoretical values. This study is therefore proposing a fundamental knowledge to extract critical behavior from complicated systems, where the exchange parameter is a periodic function of distance. © 2013 Copyright Taylor and Francis Group, LLC.