Phase coherence in 2D XY and Heisenberg models*1

Abstract

A high-precision Monte Carlo study has been made on the two-dimensional XY and Heisenberg models to make clear the nature of the low-temperature behavior of 2D classical spin models. A new type of order parameter is introduced to measure the phase coherence inherent in these models. It has been found that the phase coherence and its fluctuation can be expressed in terms of the characteristic scaling functions. The form of the scaling function in 2D XY model clearly indicate the existence of the Kosterlitz and Thouless transition. Several trials have been made to find the scaling function in 2D Heisenberg model; the most probable form is quite different from the KT form which renders some possibility that the coherent length is still finite at any nonzero temperatures.