Effective potential for the massive sine-Gordon model

S. Nagy, J. Polonyi, K. Sailer

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The infrared (IR) scaling laws for the massive sine-Gordon model (MSGM) for the number d ≤ 2 of spacetime dimensions are determined by means of the functional form of the differential renormalization group (RG) with gliding sharp cut-off k in momentum space in the local potential approximation. This generically non-perturbative method enables one to determine the flow of an arbitrary number of Fourier amplitudes (couplings) of the periodic piece of the potential for any values of the 'inverse temperature' β2. It is shown that the dimensionless couplings of the periodic piece of the blocked potential exhibit the trivial IR scaling law, ∼k-2 due to the mass term breaking periodicity explicitly. Three distinct phases are identified in the space of the bare parameters. The RG flow for phases in which the intrinsic scale kSG of the corresponding phases of the sine-Gordon model (SGM) is larger than the mass, exhibits features similar to those of the RG flow for the SGM, and the effective potentials of these phases appear as IR fixed points.

Original languageEnglish
Article numberS21
Pages (from-to)8105-8117
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number25
Publication statusPublished - Jun 23 2006


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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