A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios

Abstract

We simulate lattice models in the three-dimensional XY universality class in the low and the high temperature phase. This allows us to compute a number of universal amplitude ratios with unprecedented precision: R_Υ=0.411(2), R_B=2.83(1), R_ξ^+=0.3562(10) and R_ξ^-=0.850(5). These results can be compared with those obtained from other theoretical methods, such as field theoretic methods or the high temperature series expansion and also with experimental results for the lambda-transition of ${}^4$He. In addition to the XY model, we study the three-dimensional two-component ${\varphi }^4$ model on the simple cubic lattice. The parameter of the ${\varphi }^4$ model is chosen such that leading corrections to scaling are small.

28 pages 5 figures

References in corpus (16)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• 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
• Finite size effects on measures of critical exponents in d=3 O(N) models
• High precision Monte Carlo study of the 3D XY-universality class
• Surface and bulk transitions in three-dimensional O(n) models
• Universal Amplitude Ratios in the 3D Ising Model
• Critical specific heats of the N-vector spin models on the sc and the bcc lattices
• Universal amplitude ratios from numerical studies of the three-dimensional O(2) model
• Minimal renormalization without ε-expansion: Three-loop amplitude functions of the O(n) symmetric ϕ^4 model in three dimensions below T_c
• The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-
• Chiral perturbation theory, finite size effects and the three-dimensional $XY$ model
• Nature of Phase Transitions in a Generalized Complex |psi|^4 Model
• Minimal renormalization without epsilon-expansion: Amplitude functions in three dimensions below T_c

Cited by in corpus (19)

• Conformal dimensions via large charge expansion
• Universal amplitude ratios in the 3D Ising Universality Class
• Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models
• The specific heat, the energy density and the thermodynamic Casimir force in the neighbourhood of the lambda-transition
• The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Yet another method to compute the thermodynamic Casimir force in lattice models
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Vortex mass in the three-dimensional $O(2)$ scalar theory
• Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models
• The specific heat of thin films near the lambda-transition: A Monte Carlo study of an improved three-dimensional lattice model
• Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy
• A variance reduced estimator of the connected two-point function in the presence of a broken Z_2 symmetry
• Critical behaviours of anisotropic XY ferromagnet in the presence of random field
• Driven spin wave modes in XY ferromagnet: Nonequilibrium phase transition
• Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity
• Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition
• Nonequilibrium tricritical behaviour in anisotropic XY ferromagnet driven by elliptically polarised propagating magnetic field wave
• Equilibrium and Nonequilibrium phase transitions in continuous symmetric classical magnets