Monte Carlo simulation with Wolff algorithm for scaling behavior of two dimensional XY model with KT phase transition

Abstract

The property of XY model with its KT phase transition has been discussed in many aspects such as specific heat and magnetic susceptibility along with correlation function. Also, this is one of the original models for topological phase transition which gives a new type of phase transition without symmetry breaking. Since the calculation of these properties above can be achieved by Monte Carlo Method with Wolff algorithm, the visualization of vortex and antivortex is also an interesting task which is accomplished in this article. By successfully modeling the system and getting the step-by-step configuration, the relation between the generation of vortex and the variation of temperature can be concluded in a qualitative way. The calculation of spin correlation function shows the phase transition between disorder and quasi long-range order which represents the topological phase transition. As a reliable method, the Monte Carlo method with Wolff algorithm can be a choice of generating the training set for neural network which can calculated much more sophisticated case in a relatively short time and the transition between classical simulation and quantum simulation can be approached as mentioned in the end of this article.