Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

  • N. Defenu
  • P. Mati
  • I. G. Márián
  • I. NándoriEmail author
  • A. Trombettoni
Open Access
Regular Article - Theoretical Physics


We study the occurrence of spontaneous symmetry breaking (SSB) for O(N ) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N = 1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.


Field Theories in Lower Dimensions Spontaneous Symmetry Breaking Renormalization Group Renormalization Regularization and Renormalons 


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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • N. Defenu
    • 1
    • 2
  • P. Mati
    • 3
    • 4
    • 5
  • I. G. Márián
    • 4
  • I. Nándori
    • 4
    • 6
    • 7
    Email author
  • A. Trombettoni
    • 2
    • 1
    • 8
  1. 1.SISSATriesteItaly
  2. 2.CNR-IOM DEMOCRITOS Simulation CenterTriesteItaly
  3. 3.Budapest University of Technology and Economics, Department of Theoretical PhysicsBudapestHungary
  4. 4.University of DebrecenDebrecenHungary
  5. 5.Eötvös University, Department of Atomic PhysicsBudapestHungary
  6. 6.MTA-DE Particle Physics Research GroupDebrecenHungary
  7. 7.MTA AtomkiDebrecenHungary
  8. 8.INFN, Sezione di TriesteTriesteItaly

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