Discrete translational invariance and mass-renormalization in the two-dimensional sine-Gordon model

We consider the sine-Gordon model as a field-theory in which the interaction has a discrete translational invariance. It is shown that apart from a Gaussian contribution the Helmholtz free-energy exhibits this symmetry as well. Thus in an originally massless theory, the insertion of a mass term can be considered as a rather weak symmetry-breaking. Within the Amit-Goldschmidt-Grinstein renormalization-scheme we show that mass-renormalization is trivial.