Decimations for Two-dimensional Ising and Rotator Models

Matteo d'Achille (1) , Aernout C D van Enter (2) , Arnaud Le Ny (1)

1 LAMA - Laboratoire Analyse et de Mathématiques Appliquées
2 Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence

We extend proofs of non-Gibbsianness of decimated Gibbs measures at low temperatures to include long-range, as well as vector-spin interactions. Our main tools consist in a two-dimensional use of "Equivalence of boundary conditions" in the long-range case and an extension of Global specifications for two-dimensional vector spins.

Mots clés: Long-range Ising models; Rotator models; Gibbs measures; Renormalized measures; Non-Gibbsianness; Global specifications

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]

Matteo d'Achille, Aernout C D van Enter, Arnaud Le Ny. Decimations for Two-dimensional Ising and Rotator Models. Journal of Mathematical Physics, 2022, 63 (3), ⟨10.1063/5.0057174⟩. ⟨hal-03229089⟩