Truncation effects in the functional renormalization group study of spontaneous symmetry breaking
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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.
KeywordsField Theories in Lower Dimensions Spontaneous Symmetry Breaking Renormalization Group Renormalization Regularization and Renormalons
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- S. Stringari, Sum Rules and Bose-Einstein Condensations, in Bose-Einstein condensation, A. Griffin, D.W. Snoke and S. Stringari eds., Cambridge University Press, Cambridge (1995), p. 86 [cond-mat/9311024].
- G.S. Joyce, Critical Properties of the Spherical Model, in Phase Transitions and Critical Phenomena, vol. 2, C. Domb and M.S. Green eds., Academic Press (1972), p. 375.Google Scholar
- B. Delamotte, Introduction to the Non-Perturbative Renormalization Group, in Order, disorder and criticality. Advanced problems of phase transition theory, Y. Holovatch ed., World Scientific, Singapore (2007).Google Scholar
- E. Marchais, Infrared properties of scalar field theories, Ph.D. Thesis, University of Sussex, Brighton, U.K. and online at http://sro.sussex.ac.uk/45244/.
- V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional system possessing a continuous symmetry group, II. Quantum systems, Zh. Eksp. Teor. Fiz. 61 (1971) 1144 [Sov. Phys. JETP 34 (1972) 610].Google Scholar
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