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 the Wegner-Houghton method, and by way of the real-space RG approach. 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 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.
I. Nandori et al., "Renormalization-Group Analysis of the Generalized Sine-Gordon Model and of the Coulomb Gas for D > 3 Dimensions," Physical Review D, Particles and fields, vol. 69, no. 2, pp. 025004-1-025004-17, American Physical Society (APS), Jan 2004.
The definitive version is available at https://doi.org/10.1103/PhysRevD.69.025004
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