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Title: Asymptotic safety on the lattice: The nonlinear O(N) sigma model

We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations and a Monte Carlo demon method. In two dimensions our results verify perturbative renormalizability. In three dimensions, we determine the flow diagram of the theory for various N and different truncations and find a non-trivial fixed point, which indicates non-perturbative renormalizability. It is related to the well-studied phase transition of the O(N) universality class and characterizes the continuum physics of the model. We compare the obtained renormalization group flows with recent investigations by means of the Functional Renormalization Group. - Highlights: • We compute the global flow diagram from lattice simulations. • Truncation of the effective action may lead to artificial fixed points. • Our optimization scheme effectively reduces truncation errors. • The Wilson–Fisher fixed point is identified as a non-trivial UV fixed point. • Asymptotic safety is realized for the 3D nonlinear sigma model.
Authors:
 [1] ;  [2] ;  [1] ;  [1]
  1. Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743 Jena (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
22403420
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 349; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; ASYMPTOTIC SOLUTIONS; COMPUTERIZED SIMULATION; ERRORS; LATTICE FIELD THEORY; MONTE CARLO METHOD; NONLINEAR PROBLEMS; OPTIMIZATION; PHASE TRANSFORMATIONS; RENORMALIZATION; SIGMA MODEL