Coherent state of the 2D classical spin models

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 the 2D classical spin models. A new type of order parameter is introduced to measure the phase coherence inherent in these models. Detailed inspections of the order parameter clearly indicate that the existence of the Kosterlitz and Thouless transition in the XY model; the low-temperature behavior is in the coherent state which is fluctuationless as in the superconducting phase.