Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition

2000/08/14 by Gero von Gersdorff, G. v. Gersdorff, C. Wetterich · 7 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Flow (mathematics) #Kosterlitz–Thouless transition #Mathematical physics #Mathematics #Mechanics #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum many-body systems #Renormalization #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat #hep-lat #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevb.64.054513

published as Phys.Rev. B64 (2001) 054513 · 4 pages, 4 figures, RevTex

arxiv created 2000/08/14 · openalex publication_date 2001/07/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Kosterlitz-Thouless phase transition is described by the nonperturbative renormalization flow of the two-dimensional \ensuremathφ⁴ model. The observation of essential scaling demonstrates that the flow equation incorporates nonperturbative effects that have previously found an alternative description in terms of vortices. The duality between the linear and nonlinear \ensuremathσ model gives a unified description of the long-distance behavior for O(N) models in arbitrary dimension d. We compute critical exponents in first order in the derivative expansion.

Citations

• Exact evolution equation for the effective potential
• Critical exponents from the effective average action
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems
• Kosterlitz-Thouless Phase Transition in the Two Dimensional LinearσModel

Cited by

• Ising exponents from the functional renormalization group
• Nonperturbative Functional Renormalization-Group Approach to the Sine-Gordon Model and the Lukyanov-Zamolodchikov Conjecture
• Fundamentals of the exact renormalization group
• The nonperturbative functional renormalization group and its applications
• Non-perturbative renormalization group calculation of the scalar self-energy
• Thermodynamics in the vicinity of a relativistic quantum critical point in2+1dimensions
• Field dependence of the Yukawa coupling in the three flavor quark-meson model