Effective potential for the massive sine-Gordon model

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' beta(2). It is shown that the dimensionless couplings of the periodic piece of the blocked potential exhibit the trivial IR scaling law, similar to 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.