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Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking

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arxiv 1410.7024 v2 pith:XGZGT5N3 submitted 2014-10-26 hep-th cond-mat.stat-mech

N. Defenu , P. Mati , I. G. Marian , I. Nandori , A. Trombettoni This is my paper · ORCID
classification hep-thcond-mat.stat-mech
keywords symmetrybreakingevenfunctionalgrouprenormalizationspontaneoussystems
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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.

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  1. Ward-constrained melonic renormalization group flow for the rank-four $\phi^6$ tensorial group field theory

    hep-th 2019-08 reject novelty 4.0 of 10

    For the rank-4 φ6 tensorial group field theory, the authors derive a Ward-constrained renormalization group flow and report a nontrivial fixed point, but the fixed point's reported values violate their own consistency...

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