Critical Phenomena Study of 3D Heisenberg Magnet

Abstract

Recent discovery of several van der waals magnetic material and moire magnet introduce to us an extremely challenging and revolutionary era of 2D magnetism and correlated phenomena for low dimensional material.More often the simplest spin models which is based on inter-atomic exchange and spin-orbit coupling(SOC) potentially able to capture and explain the critical phenomena of extremely complicated correlated magnetic material.In this work we have attempted to simulate 3D Heisenberg magnet using classical Monte Carlo simulation.Our goal is to establish a new and simplest spin simulation technique which can help us to understand those van der waals magnet from its microscopic length scale.Here we have been proposing a completely new methodology of classical Monte Carlo simulation of Heisenberg spin which is based on single spin flipping Metropolis algorithm.Our state of art simulation technique potentially able to study the phase transition of isotropic XY(O(2)) and XYZ(O(3))spin model very efficiently.With this simulation technique we overcome the barrier of critical slowing down during the phase transition in a effective way and able to predict the transition temperature($T_c$) very accurately.