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arXiv · 1503.04873

Phase transitions on the Toeplitz algebras of Baumslag-Solitar semigroups

Lisa Orloff Clark·Astrid an Huef·Iain Raeburn
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Abstract

Spielberg has recently shown that Baumslag-Solitar groups associated to pairs of positive integers are quasi-lattice ordered in the sense of Nica. Thus they have tractable Toeplitz algebras. Each of these algebras carries a natural dynamics. Here we construct the equilibrium states (the KMS states) for these dynamics. For inverse temperatures larger than a critical value, there is a large simplex of KMS states parametrised by probability measures on the unit circle. At the critical value, and under a mild hypothesis, there is a phase transition in which this simplex collapses to a singleton. There is a further phase transition at infinity, in the sense that there are many ground states which cannot be realised as limits of KMS states with finite inverse temperatures.

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Lisa Orloff Clark, Astrid an Huef, Iain Raeburn. 2015-03-16. Phase transitions on the Toeplitz algebras of Baumslag-Solitar semigroups. https://arxiv.org/abs/1503.04873

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