Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

Satya Pal Singh

Satya Pal Singh Madan Mohan Malaviya University of Technology

Abstract

This paper presents a brief review of Ising’s work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained quantitative result for two-dimensional Ising model and successfully deduced the critical temperature of the system. In 1944 Onsager explicitly obtained free energy in zero fields. Though only 1dimensional formula has been derived in this review paper but Monte
Carlo simulations results verify the established part of experiment and theory and explore the temperature dependence of magnetic property of thin film in 2D case. The paramagnetic case with spin coupling coefficient J=0 and anti-ferromagnetic cases with J=0.50, 0.75 & 1.0 are studied at temperatures kT=0.20, 0.30, 0.40, 0.50, 0.60, 1.0, 1.5 & 2.0. The change in behavior from anti-ferro to para is also observed and explained at high T values. I have demonstrated data writing for application purpose by writing number 10 on a thin anti-ferromagnetic tape (i.e. 2D film).

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