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.

Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking / Defenu, Nicolò; Mati, P; Marian, Istvan Gabor; Nandori, Istvan; Trombettoni, Andrea. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2015:5(2015). [10.1007/JHEP05(2015)141]

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

Defenu, Nicolò;Marian, Istvan Gabor;Nandori, Istvan;Trombettoni, Andrea
2015-01-01

Abstract

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.
2015
2015
5
141
10.1007/JHEP05(2015)141
Defenu, Nicolò; Mati, P; Marian, Istvan Gabor; Nandori, Istvan; Trombettoni, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33147
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