Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries

Abstract

We show how decimated Gibbs measures having unbroken continuous symmetry due to the Mermin–Wagner theorem, despite their discrete equivalents exhibiting phase transition, can still become non-Gibbsian. The mechanism rests on the occurrence of a spin-flop transition with a broken discrete symmetry, once the model is constrained by the decimated spins in a suitably chosen “bad” configuration.