Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

Abstract

We reexamine the two-dimensional linear O(2) model (${\phi }^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension $η(\Tkt)\simeq 0.24$ and the stiffness jump $ρ_s(\Tkt^-)\simeq 0.64$ at the transition temperature $\Tkt$, in very good agreement with the exact results $η(\Tkt)=1/4$ and $ρ_s(\Tkt^-)=2/π$, as well as an essential singularity of the correlation length in the high-temperature phase as $T\to \Tkt$.

v2) Final version as published (with revised title): 10 pages, 10 figures

References in corpus (9)

• Exact evolution equation for the effective potential
• Monte Carlo study of two-dimensional Bose-Hubbard model
• The critical exponents of the superfluid transition in He4
• Superfluid behaviour of a two-dimensional Bose gas
• From local to critical fluctuations in lattice models: a non-perturbative renormalization-group approach
• Universal thermodynamics of a two-dimensional Bose gas
• Renormalization group flow for fermionic superfluids at zero temperature
• Superfluid Bose gas in two dimensions
• Functional renormalization group for d-wave superconductivity in Hubbard type models

Cited by in corpus (26)

• Long-range interacting quantum systems
• Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach
• Nonperturbative renormalization group treatment of amplitude fluctuations for $|\phi {|}^4$ topological phase transitions
• Interplay of spin waves and vortices in the 2D XY model at small vortex-core energy
• Dual lattice functional renormalization group for the Berezinskii-Kosterlitz-Thouless transition: irrelevance of amplitude and out-of-plane fluctuations
• Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at $T>0$
• Scaling relations and multicritical phenomena from Functional Renormalization
• Nonperturbative functional renormalization-group approach to transport in the vicinity of a $(2+1)$-dimensional O($N$)-symmetric quantum critical point
• Universal behavior of coupled order parameters below three dimensions
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• On the nature of the Schmid transition in a resistively shunted Josephson junction
• Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group
• Relativistic Mott transitions and finite-temperature effects of quantum criticality in Dirac semimetals
• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
• Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization
• Functional renormalization-group approach to the Pokrovsky-Talapov model via modified massive Thirring fermion model
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• New renormalization group study of the 3-state Potts model and related statistical models
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Amplitude, phase, and topological fluctuations shaping the complex phase diagram of two-dimensional superconductors
• Helicity modulus in the bilayer XY model by worm algorithm
• Tunneling with physics-informed RG flows in the anharmonic oscillator
• FRG analysis for a relativistic BEC in arbitrary spatial dimensions
• Low-temperature behavior of the $O(N)$ models below two dimensions
• Higher-derivative four-dimensional sine-Gordon model