Truncation effects in the functional renormalization group study of spontaneous symmetry breaking
Year: 2015
Authors: Defenu N., Mati P., Māriān I.G., Nāndori I., Trombettoni A.
Autors Affiliation: SISSA, I-34136 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy; Budapest Univ Technol & Econ, Dept Theoret Phys, H-1111 Budapest, Hungary; Univ Debrecen, H-4010 Debrecen, Hungary; Eotvos Lorand Univ, Dept Atom Phys, H-1117 Budapest, Hungary; MTA DE Particle Phys Res Grp, H-4001 Debrecen, Hungary; MTA Atomki, H-4001 Debrecen, Hungary; Ist Nazl Fis Nucl, Sez Trieste, I-34136 Trieste, Italy.
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.
Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS
Volume: (5) Pages from: 141-1 to: 141-22
More Information: We thank A. Codello, G. Gori, E. Marchais, J.M. Pawlowski and D. Zappala for discussions. We are also grateful to A. Rancon for very useful comments on the effects of the truncation around the minimum. This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TAMOP-4.2.4.A/2-11/1-2012-0001 National Excellence Program, by the TAMOP 4.2.1./B-09/1/KONV2010-0007 project and also through the project Supercomputer, the national virtual lab (grant no.: TAMOP-4.2.2.C-11/1/KONV-2012-0010). A.T. acknowledges support from the Italian PRIN Fenomeni quantistici collettivi: dai sistemi fortemente correlati ai simulatori quantistici (PRIN 2010 2 010LLKJBX). Support from the CNR/MTA Italy-Hungary 2013-2015 Joint Project Non-perturbative field theory and strongly correlated systems is gratefully acknowledged.KeyWords: Field Theories in Lower Dimensions; Spontaneous Symmetry Breaking; Renormalization Group; Renormalization Regularization and RenormalonsDOI: 10.1007/JHEP05(2015)141Citations: 19data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)