@article{db85f6fdc5b94e3d882a397d8436fce2,
title = "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.",
author = "Matteo D'Achille and {Van Enter}, {Aernout C.D.} and {Le Ny}, Arnaud",
note = "Funding Information: We thank the referee for helpful remarks. Our research has been partially carried out within the CNRS IRP B{\'e}zout-Eurandom “Random Graph, Statistical Mechanics and Networks,” supported by Laboratory LAMA (Grant No. CNRS UMR8050), B{\'e}zout Federation (Grant No. CNRS Unit FR3522), Labex B{\'e}zout (Grant No. ANR-10-LABX-58), and Eurandom (TU/e Eindhoven). A.C.D.v.E. thanks the Universit{\'e} Paris-Est Creteil for its hospitality during a research visit. Publisher Copyright: {\textcopyright} 2022 Author(s).",
year = "2022",
month = dec,
doi = "10.1063/5.0103163",
language = "English",
volume = "63",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "AMER INST PHYSICS",
number = "12",
}