RENORMALIZATION, FREEZING PHASE TRANSITIONS AND FIBONACCI QUASICRYSTALS.

Henk Bruin (1) , Renaud Leplaideur (2)

1 Faculty of Mathematics [Vienna]
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

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

Mots clés: Phase transition; thermodynamic formalism; substitution; renormalization; fibonacci numbers

Domaines: Systèmes dynamiques [math.DS]

Henk Bruin, Renaud Leplaideur. RENORMALIZATION, FREEZING PHASE TRANSITIONS AND FIBONACCI QUASICRYSTALS.. 2013. ⟨hal-00867920⟩