Periodic Higgs Potential and the Sine-Gordon Universality Class

A periodic self-interaction is proposed as a possible extension of the standard model Higgs potential. Using the usual parametrisation of the field around the first minimum, one recovers the Lagrangian of the Higgs sector but with a periodic self-interaction term for a single-component real scalar field. The exact phase structure of the periodic scalar theory, i.e., the sine-Gordon model has been mapped out by the functional renormalization group method in arbitrary dimension and it is shown that the model has a single (broken) phase for d>2. Results are used to study the phase structure of the equivalent neutral Coulomb gas and to demonstrate that the isotropic XY spin model belongs to a different universality class for d>2.