Phase Transitions in Two-Dimensional Spin Systems

Abstract

The first nine coefficients have been derived in the exact high temperature expansion of the fluctuation in the long range order in the XY model on the triangular and square lattices. For the triangular lattice seven coefficients have also been obtained in the expansion of the fourth-order fluctuation. The method of conformal transformations has been developed in a form suitable for the analysis of series of this type. Clear evidence is obtained in favor of a phase transition for which the critical index of the fluctuations is γ ≈ 3/2. The critical temperatures kTC/J for the triangular and square lattices are 1.500 ± 0.006 and 0.900 ± 0.006 respectively.