Correlations in the low-temperature phase of the two-dimensional XY model

Abstract

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with fixed boundary conditions. Using a conformal mapping it is very easy to deduce the exponent eta_sigma(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of eta_sigma(T) is obtained numerically with a good accuracy up to the Kosterlitz-Thouless transition temperature. At very low temperatures, a good agreement is found with Berezinskii's harmonic approximation. Surprisingly, we show some evidence that there are no logarithmic corrections to the behaviour of the order parameter density profile (with symmetry breaking surface fields) at the Kosterlitz-Thouless transition temperature.

7 pages, 2 eps figures

Cited by in corpus (14)

• Critical temperature for the two-dimensional attractive Hubbard Model
• Influence of quenched dilution on the quasi-long-range ordered phase of the 2d XY model
• Introduction to topological defects: from liquid crystals to particle physics
• Bulk and surface properties in the critical phase of the two-dimensional XY model
• Scaling behavior of a square-lattice Ising model with competing interactions in a uniform field
• Evidence for a topological transition in nematic-to-isotropic phase transition in two dimensions
• Quasi-long-range ordering in a finite-size 2D Heisenberg model
• Topological transition in a two-dimensional model of liquid crystal
• Disordered two-dimensional superconductors: roles of temperature and interaction strength
• Multiple Transitions of Coupled Atom-Molecule Bosonic Mixtures in Two Dimensions
• Biexciton Condensation in Electron-hole Doped Hubbard Bilayers -- A Sign-Problem-Free Quantum Monte Carlo Study
• Numerical investigation of logarithmic corrections in two-dimensional spin models
• Phase diagram of a three-dimensional dipolar Ising model with textured Ising axes
• Scanning the critical fluctuations -- application to the phenomenology of the two-dimensional XY-model --