  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.
