Almost Gibbsian Measures on a Cayley Tree

TL;DR

This paper studies the renormalized measures of the ferromagnetic Ising model on Cayley trees under a majority rule transformation, showing they are Almost Gibbsian at all temperatures, extending understanding of non-Gibbsian phenomena.

Contribution

It demonstrates that the transformed measures remain Almost Gibbsian across all temperatures, providing a new perspective on phase behavior in Cayley tree models.

Findings

Renormalized measures are Almost Gibbs at any temperature.

Majority rule transformation leads to non-Gibbsian measures.

Extension of Gibbsian properties to transformed Cayley tree models.

Abstract

We consider the ferromagnetic n.n Ising model on Cayley trees in absence of external fields submitted to a modified majority rule transformation with overlapping cells already known to lead to non-Gibbsian measures. We describe the renormalized measures within the Generalized Gibbs framework and prove that they are Almost Gibbs at any temperature.