Ising exponents from the functional renormalization group

2010/09/10 by Daniel F. Litim, Dario Zappalà, Dario Zappalá · 7 citations
Mathematics · Physics and Astronomy · #Critical exponent #Critical phenomena #Criticality #Curse of dimensionality #Functional renormalization group #Geometry #Ising model #Mathematical physics #Mathematics #Monte Carlo method #Phase transition #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization #Renormalization group #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #hep-th

paper · pdf · doi:10.1103/physrevd.83.085009

published as Phys.Rev.D83:085009,2011 · 24 pages, 3 figures, 7 tables

arxiv created 2010/09/10 · openalex publication_date 2011/04/07 · arxiv updated 2011/04/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the 3d Ising universality class using the functional renormalization group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and antisymmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross correlations of scaling exponents, their dependence on dimensionality, and the numerical convergence of the derivative expansion. Collecting all available data from functional renormalization group studies to date, we estimate that systematic errors are in good agreement with findings from Monte Carlo simulations, ϵ-expansion techniques, and resummed perturbation theory.

Citations

• The renormalization group and the ε expansion
• The Effective Average Action Beyond First Order
• Exact renormalization group equations: an introductory review
• Exact evolution equation for the effective potential
• Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Gauge invariance and background field formalism in the exact renormalisation group
• Critical exponents of theN-vector model
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order \∂⁴

Cited by

• Quark-meson-diquark model for two-color QCD
• The nonperturbative functional renormalization group and its applications
• Universal Location of the Yang-Lee Edge Singularity in O(N) Theories
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• Phases of supersymmetricO(N)theories
• Heat kernel coefficients on the sphere in any dimension
• Solving the 3d Ising Model with the Conformal Bootstrap II. c c -Minimization and Precise Critical Exponents