Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models

Abstract

We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component ϕ^4 model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L_0=32 lattice spacings. In the short direction of the lattice free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U_4, the second moment correlation length over the lattice size ξ_{2nd}/L, the ratio of the partition functions with anti-periodic and periodic boundary conditions Z_a/Z_p and the helicity modulus Υclearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L_0 of the film. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L_0 and the transversal correlation length ξ_T in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L_0: [L_{0,KT}/ξ_T]^* = 1.595(7). This results can be compared with experimental results on thin films of 4He near the λ-transition.

45 pages, 7 figures

References in corpus (22)

• Critical Phenomena and Renormalization-Group Theory
• Critical behavior of the three-dimensional XY universality class
• The critical exponents of the superfluid transition in He4
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Finite size effects on measures of critical exponents in d=3 O(N) models
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Monte Carlo simulation results for critical Casimir forces
• High precision Monte Carlo study of the 3D XY-universality class
• The Thermodynamic Casimir Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Surface and bulk transitions in three-dimensional O(n) models
• Universal Amplitude Ratios in the 3D Ising Model
• Universal amplitude ratios from numerical studies of the three-dimensional O(2) model
• Crossover from Two- to Three-Dimensional Behavior in Superfluids
• Direct Monte Carlo Measurement of the Surface Tension in Ising Models
• A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios
• Boundary effects in superfluid films
• The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-
• Heat capacity scaling function for confined superfluids
• Nature of Phase Transitions in a Generalized Complex |psi|^4 Model
• Scaling of the superfluid density in superfluid films

Cited by in corpus (16)

• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Finite-size scaling at quantum transitions
• The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition
• Large-$n$ approach to thermodynamic Casimir effects in slabs with free surfaces
• Critical behavior in the presence of an order-parameter pinning field
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Yet another method to compute the thermodynamic Casimir force in lattice models
• Critical Casimir force in the presence of random local adsorption preference
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist
• Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields
• Non-universal Casimir Effect in Saturated Superfluid ${}^4$He Films at T${}_{\lambda }$