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

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

2003-12-17

arxiv.org/abs/math/0312344v4

Mathematics

Probability

16 Pages

Scientific paper

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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