Renormalization of periodic potentials - art. no. 045022

The renormalization of the periodic potential is investigated in the framew ork of the Euclidean one-component scalar field theory by means of the diff erential RG approach. Some known results about the sine-Gordon model are re covered in an extremely simple manner. There are two phases: an ordered one with asymptotical freedom and a disordered one where the model is nonrenor malizable and trivial. The order parameter of the periodicity, the winding number, indicates spontaneous symmetry breaking in the ordered phase where the fundamental group symmetry is broken and the solitons acquire dynamical stability. It is argued that the periodicity and the convexity are such st rong constraints on the effective potential that it always becomes flat. Th is flattening is reproduced by integrating out the RG equation.