Phase Transition Of Antiferromagnetic 3-state Potts Model Based On Worm Algorithm

Phase transition and critical phenomena are important branches of statistical physics.The critical phenomenon is the singular behavior of the physical system at the point of transformation.The Potts model plays an important role in the field of phase transition research and all kinds of phase transition can be produced in the Potts model.The study of it could better understand the nature of phase transitionMonte Carlo simulation is a numerical simulation method for studying critical phe-nomena.In this paper,we use the efficient worm algorithm in Monte Carlo simulation to study the antiferromagnetic 3-state Potts model.The phase transition of this model is investigated when vortex excitation changes.First,we briefly introduce the basic concepts of continuous phase transformation,scaling theory,and some classical statistical models.Then,we introduce the main ideas of monte carlo simulation,and introduce some commonly used simulation methods,metropolis algorithm,cluster algorithm,and worm algorithm,and explain the design ideas of these algorithms.Finally,we study the antiferromagnetic Potts model on the two-dimensional square lattice.We apply the worm algorithm to this model,and simulate the system under two conditions that the vortex excitation is suppressed and promoted,and the phase diagram of the system is drawn.We found that two BKT transitions with different critical ex*-ponents can be found in the system,whether to promote or suppress the excitation of the vortex structure on the antiferromagnetic Potts model.Moreover,when we promote the vortex excitation,the system also takes place a ising-type phase transition from the vortex lattice phase to the disordered phase,and at low temperature the system is in the superposition state of the quasi-long-order phase and the vortex lattice phase.