Phase Transition in the Two Dimensional Classical XY Model

Abstract

For the two dimensional classical XY model we present extensive high -temperature -phase bulk data extracted based on a novel finite size scaling (FSS) Monte Carlo technique, along with FSS data near criticality. Our data verify that $\eta =1/4$ sets in near criticality, and clarify the nature of correction to the leading scaling behavior. However, the result of standard FSS analysis near criticality is inconsistent with other predictions of Kosterlitz's renormalization group approach.

Significant changes in the text and the figures. To appear in Phys. Lett. A Hard copies of seven figures are available upon request

References in corpus (6)

• Finite-Size Scaling at $\xi /L\gg 1$
• Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at Correlation Length $10^5$
• High Precision Renormalization Group Study of the Roughening Transition
• Logarithmic Corrections to Scaling in the Two Dimensional $XY$--Model
• Numerical Computation of Finite Size Scaling Functions: An Alternative Approach to Finite Size Scaling
• Scaling behavior of the four-point renormalized coupling constant in the two dimensional O(2) and O(3) non-linear sigma models

Cited by in corpus (6)

• The Kosterlitz-Thouless Universality Class
• Essential finite-size effect in the 2D XY model
• Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
• Invaded cluster simulations of the XY model in two and three dimensions
• Bulk and surface properties in the critical phase of the two-dimensional XY model
• Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model