Abstract:
In this talk i will present recent results obtained in collaboration with Loren Coquille (Grenoble, France) and Christof Külske (Bochum, Germany) [1,2] where we extend previous results of Gandolfo et al. [3,4] from Ising systems to general ferromagnetic finite-spin models. We focus on Gibbs measures obtained with free boundary conditions ('free states') in the very low temperature regions where we prove its non-extremality for a wide class of models including q-states Potts and clock models but also slight non-symmetric perturbations of them ('central states'). We also describe in general the non-trivial, continuous, extremal decomposition of these states at low temperature and show in particular that their decomposition into uncountably many glassy states in finite-spin models on trees is a generic phenomenon and does not rely on symmetries of the Hamiltonian.
References :
[1] L. Coquille, C. Külske, A. Le Ny
Extremal inhomogeneous Gibbs States for the SOS-models and finite-spin models on trees.
Journal of Statistical Physics 191:71, 2023
[2] L. Coquille, C. Külske, A. Le Ny
Continuity of the extremal decomposition of the free state for finite-spin models on Cayley trees.
ArXiv October 2023, submitted.
[3] D. Gandolfo, J. Ruiz, S. Shlosman.
A manifold of pure GIbbs states of the Ising model on a Cayley tree.
Journal of Statistical Physics 148:999--1005, 2012.
[4] D. Gandolfo, C. Maes, J. Ruiz, S. Shlosman.
Glassy states: The free Ising model on a tree.
Journal of Statistical Physics 180, no 5/6:227-237, 2020.
Biography:
Arnaud Le Ny is full Professor at Université Paris Est, within the CNRS Laboratory LAMA and university UPEC, whose research in Mathematical Statistical Mechanics focus on general properties of Gibbs measures of general spin and disordered systems. He obtained a PhD from University of Rennes (France) in 2000 and a french habilitation (HDR) from University Paris Sud in 2010. Before its academic position in Paris-Est, he has been assistant professor at University Paris-Sud (CNRS Laboratory of Mathematics Orsay) from 2003 to 2013, temporary assistant professor at University of Rouen (France) in 2000-2001 and postdoctorate at EURANDOM (Eindhoven, Nederland) from 2001 to 2003. He spent its academic year 2017-2018 at EURANDOM as a CNRS visitor and as a formal EURANDOM ambassador he drives a small CNRS International Research Project between Paris-Est and EURANDOM.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.