Decimations for One- and Two-dimensional Ising and Rotator Models II: Continuous versus Discrete Symmetries
arXiv:2206.06990 · doi:10.1063/5.0103163
Abstract
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can 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.
16 pages, 1 figure (updated)