Decimations for Two-dimensional Ising and Rotator Models I

TL;DR

This paper extends the understanding of non-Gibbsianness in decimated Gibbs measures for 2D Ising and rotator models, including long-range and vector-spin interactions, using advanced boundary condition equivalences and global specifications.

Contribution

It introduces new proofs for non-Gibbsianness in 2D models with long-range and vector-spin interactions, expanding previous results.

Findings

Non-Gibbsianness established for extended models

Use of boundary condition equivalence in long-range interactions

Extension of global specifications for vector spins

Abstract

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.