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arXiv · 1309.7934

Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals

Henk Bruin·Renaud Leplaideur
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Abstract

We examine the renormalization operator determined by the Fibonacci substitution. We exhibit a fixed point and determine its stable leaf (under iteration of the operator). Then, we study the thermodynamic formalism for po- tentials in this stable leaf, and prove they have a freezing phase transition, with ground state supported on the attracting quasi-crystal associated to the Fibonacci substitution

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Henk Bruin, Renaud Leplaideur. 2013-09-30. Renormalization, Freezing Phase Transitions and Fibonacci Quasicrystals. https://arxiv.org/abs/1309.7934

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