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Nonuniqueness for specifications in $\ell^{2+ε}$

Noam Berger·Christopher Hoffman·Vladas Sidoravicius
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Abstract

For every $p>2$, we construct a regular and continuous specification ($g$-function), which has a variation sequence that is in $l^p$ and which admits multiple Gibbs measures. Combined with a recent result of Johansson and Oberg, this determines the optimal modulus of continuity for a specification which admits multiple Gibbs measures.

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Noam Berger, Christopher Hoffman, Vladas Sidoravicius. 2005-02-07. Nonuniqueness for specifications in $\ell^{2+ε}$. https://arxiv.org/abs/math/0312344

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