Monte Carlo and coarse graining renormalization studies for the XY model with cubic anisotropy

The XY model with cubic anisotropy is studied using a Monte Carlo coarse graining renormalization calculation. Particular emphasis is placed on the accuracy of phase diagrams and the finite-size effects on the phase transition. Non-universal behavior of the correlation-length critical exponent v with respect to variation of the cubic anisotropic field h4 is analysed and an empirical formula v = [1 − exp(− ch4)]−1 is proposed. The results are discussed with reference to the surface reconstruction phase transition of the W(001) surface.