Non-uniqueness for specifications in

Abstract

For every $p>2$, we construct a regular and continuous specification ($g$-function), which has a variation sequence that is in $\ell ^{p}$ and which admits multiple Gibbs measures. Combined with a result of Johansson and Öberg [Square summability of variations of $g$-functions and uniqueness in $g$-measures. Math. Res. Lett.10(5–6) (2003), 587–601], this determines the optimal modulus of continuity for a specification which admits multiple Gibbs measures.