Relaxational dynamics study of the classical Heisenberg spin XY model in spherical coordinate representation -: art. no. 024406

The two- and three-dimensional classical Heisenberg spin XY (CHSXY) models, with the spherical coordinates of spins taken as dynamic variables, are numerically investigated. We allow the polar theta and azimuthal phi angles to have uniform values in [0,pi) and [- pi,pi). respectively, and the static universality class is shown to be identical to the classical XY model with two-component spins, as well as the CHSXY model with a different choice of dynamic variables, conventionally used in the literature. The relaxational dynamic simulation reveals that the dynamic critical exponent z is found to have the value z approximate to2.0 for both two and three dimensions, in contrast to z approximate tod/2 (d= spatial dimension) found previously with spin dynamics simulation of the conventional CHSXY model. Comparisons with the usual two-component classical XY model are also made.