Thermodynamics of the Two-Dimensional Spin-1/2 XY Model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto several three-dimensional Ising models with complicated many-spin interactions. This hierarchy of Ising-like models is studied by means of analytic and Monte Carlo techniques. We demonstrate that the sequence of these Ising models can be used to calculate accurately the thermodynamics of the two-dimensional spin-1/2 XY model. By calculating the specific heat, spin correlation functions, susceptibilities and a disorder parameter, we address the question of the nature of the phase transition in the two-dimensional spin-1/2 XY model