Séminaire Probabilités et Statistiques
External inhomogeneous Gibbs states on trees
Feb. 2023
Intervenant : Loren Coquille
Institution : Université Grenoble Alpes
Heure : 14h00 - 15h00
Lieu : 3L15

Statistical mechanics models on trees have been studied for almost fifty years, motivations coming from the theory of spin glasses or information theory.


In the case of the Ising model, unlike the lattice case, on the tree the behavior of the free state (corresponding to empty boundary conditions) is very rich. Indeed, the free state is extremal below the critical temperature, until the spin-glass temperature 0<\uD835\uDC47\uD835\uDC46\uD835\uDC3A<\uD835\uDC47\uD835\uDC50, below which there are infinitely many pure states.


I will discuss the case of ℤ-valued p-SOS-models and ferromagnetic finite-spin models on regular trees. This includes the classical SOS-model, the discrete Gaussian and the Potts model.


In a joint work with Christof Kuelske and Arnaud Le Ny, we exhibit large sets of inhomogeneous ground state configurations, and prove that there are associated extremal inhomogeneous states at low temperature.


This constitutes a generalisation of the states initially introduced by Gandolfo, Ruiz and Shlosman in 2012 in the case of the Ising model, which play a key role in the decomposition of the Ising free state.

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