On the zero-temperature limit of Gibbs states

Abstract

We exhibit Lipschitz (and hence Hölder) potentials on the full shift $\{0,1{\}}^{\mathbb{N}}$ such that the associated Gibbs measures fail to converge as the temperature goes to zero. Thus there are "exponentially decaying" interactions on the configuration space $\{0,1{\}}^{\mathbb{Z}}$ for which the zero-temperature limit of the associated Gibbs measures does not exist. In higher dimension, namely on the configuration space $\{0,1{\}}^{{\mathbb{Z}}^d}$, $d\ge 3$, we show that this non-convergence behavior can occur for finite-range interactions, that is, for locally constant potentials.

The statement of Theorem 1.2 is more accurate and some new comment follow it

References in corpus (1)

• Chaotic temperature dependence at zero temperature

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