Second-order and fluctuation-induced first-order phase transitions with functional renormalization group equations

Kenji Fukushima, Kazuhiko Kamikado, and Bertram Klein
Phys. Rev. D 83, 116005 – Published 17 June 2011

Abstract

We investigate phase transitions in scalar field theories using the functional renormalization group (RG) equation. We analyze a system with U(2)×U(2) symmetry, in which there is a parameter λ2 that controls the strength of the first-order phase transition driven by fluctuations. In the limit of λ20, the U(2)×U(2) theory is reduced to an O(8) scalar theory that exhibits a second-order phase transition in three dimensions. We develop a new insight for the understanding of the fluctuation-induced first-order phase transition as a smooth continuation from the standard RG flow in the O(8) system. In our view from the RG flow diagram on coupling parameter space, the region that favors the first-order transition emerges from the unphysical region to the physical one as λ2 increases from zero. We give this interpretation based on the Taylor expansion of the functional RG equations up to the fourth order in terms of the field, which encompasses the ε-expansion results. We compare results from the expansion and from the full numerical calculation and find that the fourth-order expansion is only of qualitative use and that the sixth-order expansion improves the quantitative agreement.

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  • Received 16 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.116005

© 2011 American Physical Society

Authors & Affiliations

Kenji Fukushima

  • Department of Physics, Keio University, Kanagawa 223-8522, Japan

Kazuhiko Kamikado

  • Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

Bertram Klein

  • Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany

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Issue

Vol. 83, Iss. 11 — 1 June 2011

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