Renormalization group analysis of the generalized sine-Gordon model and of the Coulomb gas for d greater than or equal to three-dimensions

Oct, 2003
23 pages
Published in:
  • Phys.Rev.D 69 (2004) 025004
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Abstract:
Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.
  • 11.10.Gh
  • 11.10.Hi
  • 11.10.Kk
  • sine-Gordon model
  • gas: Coulomb
  • dimension: >=3
  • renormalization group: transformation
  • partition function
  • gas: vortex
  • effective potential