8 papers · 1 filter
Extremal Ising Gibbs States on Lobachevsky lattices
Matteo D'Achille, Loren Coquille, Arnaud Le Ny
We exhibit an uncountable family of extremal inhomogeneous Gibbs measures of the low temperature Ising model on regular tilings of the hyperbolic plane. These states arise as low t…
Quantitative delocalisation for the Gaussian and -SOS long-range chains
Loren Coquille, Paul Dario, Arnaud Le Ny
The goal of this article is to study quantitatively the localisation/delocalisation properties of the discrete Gaussian chain with long-range interactions. Specifically, we conside…
Absence of shift-invariant Gibbs states (delocalisation) for one-dimensional -valued fields with Long-Range interactions
Loren Coquille, Aernout C. D. van Enter, Arnaud Le Ny +1
We show that a modification of the proof of our paper [CvELNR18], in the spirit of [FP81], shows delocalisation in the long-range Discrete Gaussian Chain, and generalisations there…
Continuity of the extremal decomposition of the free state for finite-spin models on Cayley trees
Loren Coquille, Christof Kuelske, Arnaud Le Ny
We prove the continuity of the extremal decomposition measure of the free state of low temperature Potts models, and more generally of ferromagnetic finite-spin models, on a regula…
Stochastic individual-based models with power law mutation rate on a general finite trait space
Loren Coquille, Anna Kraut, Charline Smadi
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possib…
Absence of Dobrushin states for long-range Ising models
Loren Coquille, Aernout C. D. van Enter, Arnaud Le Ny +1
We consider the two-dimensional Ising model with long-range pair interactions of the form with , mostly when . We show that Dobrushin sta…