Critical Properties of the Two-Dimensional Spin-1/2 XY Ferromagnet

Abstract

Critical phenomena of the two-dimensional XY model have been arousing a great deal of interest for a couple of decades [1,2] because of the model’s marginal feature that the internal degree of freedom is two, which is a critical value in two dimensions. It is proved that in two dimensions a continuous symmetry breaks the long-range order at finite temperatures [3]. Nevertheless, the possibility of the existence of a phase transition without long-range order was suggested by numerical investigations [4]. Thereafter, the nature of phase transitions of such systems, namely the XY and Heisenberg models, has been studied by various methods in classical systems. While the Heisenberg model turned out to have no phase transition at finite temperatures [5], it has been found that a marginal type of phase transition, known as the Kosterlitz-Thouless transition, takes place where a vortex, namely a topological singularity of this system, plays an important role [6–9].