Free energy and uniqueness in 1D spin systems with random Hamiltonians

CDSNS Colloquium
Friday, April 28, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Cesar Octavio Maldonado Ahumada – IPICYT –
Alex Blumenthal, Jorge Gonzalez


Abstract: In this talk, I will discuss problems and results in the rigorous statistical mechanics of particle systems in a one-dimensional lattice.
I will briefly describe the classical examples, such as the Ising model and its various generalizations concerning the
existence of the free energy, thermodynamic limit and the phase transition phenomenon.
Towards the end of the talk, I will talk about a recent work in collaboration with Jorge Littin, on a generalization of the
Khanin and Sinai model with random interactions for which one can prove that there exists a critical behavior in the free
energy for some parameters of the model and on the other side one can also have uniqueness of the equilibrium state.