Monte Carlo studies of the two-dimensional XY model with four-fold anisotropy
Truong Thi Bach Yen (College of Natural Sciences, Can Tho University, Can Tho, Vietnam, Faculty of Natural Sciences Teacher Education, Dong Thap University, Dong Thap, Vietnam)
; Le Thi Thao Vien (Faculty of Natural Sciences, Quy Nhon University, Quy Nhon, Vietnam); Nguyen Tri Tuan (College of Natural Sciences, Can Tho University, Can Tho, Vietnam); Dinh Manh Tien (College of Natural Sciences, Can Tho University, Can Tho, Vietnam); Nguyen Duc Dung (School of Materials Science and Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam); et al - Show all 11 authors
Early theoretical studies of the two-dimensional XY model with four-fold anisotropy (XY h 4) predicted that any finite anisotropy should completely suppress Kosterlitz–Thouless (KT) transition of the isotropic system and replace it with a second-order phase transition. This prediction is inconsistent with Monte Carlo (MC) simulations, which suggested KT-like behavior at weak anisotropy. To resolve this discrepancy, we performed large-scale MC simulations to systematically examine the XY h 4 model across a wide range of anisotropic strengths. Our results indicate that while weak anisotropy can mimic KT behavior in small systems, a detailed finite-size scaling analysis of larger systems reveals that the temperature derivative of Binder ratio and the correlation length ratio displays scaling behaviors characteristic of a second-order transition even at the weak h 4 values. The critical exponent ν is non-universal and varies continuously with h 4 from weak to strong anisotropy. These findings confirm that XY h 4 model exhibits a second-order phase transition for weak finite anisotropy, effectively reconciling theoretical predictions with numerical observations.
