Study influence of symmetry-breaking field h3 to phase transition of the 2D XY model

Abstract

Abstract: Two dimensional magnetic materials have experimental critical exponents that often have different critical exponent, not belonging to the Ising universal class nor to the XY universal class, but their values lies in a “universal window”, bounded by the Ising and XY critical exponent. The XYh_q model is introduced to study these materials. Theoretically, XYh_q model has been studied by using renormalization group and numerical simulation. In this model, the authors have shown: for q≤ 4, it has only the Ising phase transition; for q> 4, it has KT phase transition depending on the value of q. However, experimental critical exponents have unusual behavious even with anisotropy q ≤ 4. Therefore, we study the phase transition phenomena of XYh₃ model depending on the intensity of anisotropic crystal fields (h₃) using extensive Monte Carlo simulation. The results show that the phase transition of XYh₃ depends on the intensity of h₃: for h₃> 0.01 the model has a second-order phase transition and the phase transition temperature decreases as the crystal field strength decreases; for h₃ ≤ 0.01 The model still has a second-order phase transition, but the phase transition temperature is constant and equal to the KTphase transition temperature.