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 T_C = 2.2684 ± 0.0006 J/k_B for ferromagnetic system and T_C = 2.2689 ± 0.0003 J/k_B for anti-ferromagnetic system which match well with the exact theoretical value T_C ≈ 2.269 J/k_B . 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.

Keywords:

• Critical temperature
• finite size scaling
• harmonic order parameter

Acknowledgment

The authors wish to acknowledge financed support from the Graduate School of Chiang Mai University.