Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions

Abstract

We investigate the general features of the renormalization-group flow at the Berezinskii-Kosterlitz-Thouless (BKT) transition, providing a thorough quantitative description of the asymptotc critical behavior, including the multiplicative and subleading logarithmic corrections. For this purpose, we consider the RG flow of the sine-Gordon model around the renormalizable point which describes the BKT transition. We reduce the corresponding beta-functions to a universal canonical form, valid to all perturbative orders. Then, we determine the asymptotic solutions of the RG equations in various critical regimes: the infinite-volume critical behavior in the disordered phase, the finite-size scaling limit for homogeneous systems of finite size, and the trap-size scaling limit occurring in 2D bosonic particle systems trapped by an external space-dependent potential.

16 pages, refs added

References in corpus (42)

• Many-Body Physics with Ultracold Gases
• Cold bosonic atoms in optical lattices
• Critical Phenomena and Renormalization-Group Theory
• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Observation of scale invariance and universality in two-dimensional Bose gases
• Observation of a 2D Bose-gas: from thermal to quasi-condensate to superfluid
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics
• Multicritical behavior in the fully frustrated XY model and related systems
• Computing the Roughening Transition of Ising and Solid-On-Solid Models by BCSOS Model Matching
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs
• Critical behavior and scaling in trapped systems
• Trap-size scaling in confined particle systems at quantum transitions
• Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Logarithmic Corrections in the 2D XY Model
• Four-point renormalized coupling constant in O(N) models
• A strong-coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices
• The Kosterlitz-Thouless Universality Class
• Logarithmic Corrections to Scaling in the Two Dimensional $XY$--Model
• A quantitative study of the Kosterlitz-Thouless phase transition in a system of two-dimensional plane rotators ( XY model ) by high temperature expansions through ${\beta }^{20}$
• The Binder Cumulant at the Kosterlitz-Thouless Transition
• Effective potential in three-dimensional O(N) models
• Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions
• High temperature study of the Kosterlitz-Thouless phase transition in the XY model on the triangular lattice
• Does the XY Model have an integrable continuum limit?
• High-temperature expansion of the magnetic susceptibility and higher moments of the correlation function for the two-dimensional XY model
• Critical Behaviour of the Two Dimensional Step Model
• Two-loop beta functions of the Sine-Gordon model
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Magnetic and glassy transitions in the square-lattice XY model with random phase shifts
• Critical parameters from trap-size scaling in trapped particle systems
• Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models
• Kosterlitz Thouless Universality in Dimer Models
• Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles
• Finite-size scaling behavior in trapped systems
• Quasi-long-range order in trapped systems
• Scaling behaviour of trapped bosonic particles in two dimensions at finite temperature
• Numerical simulations of a two-dimensional lattice grain boundary model

Cited by in corpus (25)

• Finite-size scaling at quantum transitions
• Coherent and dissipative dynamics at quantum phase transitions
• Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Normal form for renormalization groups
• Quench dynamics of an ultracold two-dimensional Bose gas
• Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Bose-Einstein condensation and critical behavior of two-component bosonic gases
• Truncation effects in the charge representation of the O(2) model
• Competing Orders and Unconventional Criticality in the Su-Schrieffer-Heeger Model
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Berezinskii-Kosterlitz-Thouless Transition with a Constraint Lattice Action
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Reentrance of Berezinskii-Kosterlitz-Thouless-like transitions in three-state Potts antiferromagnetic thin film
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories
• Weird scaling for 2-D avalanches: Curing the faceting, and scaling in the lower critical dimension
• Exact Renormalization Group and Sine Gordon Theory
• Percolation of the two-dimensional XY model in the flow representation
• Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors
• First and second sound in a two-dimensional dilute Bose gas across the Berezinskii-Kosterlitz-Thouless transition
• Holographic Beta functions for the Generalized Sine Gordon Theory
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions