Contour methods for -dimensional Long-Range Ising Model.

Resumen:  On the -dimensional lattice with , the phase transition of the nearest-neighbor ferromagnetic Ising model can be proved by using Peierls argument, that requires a notion of contours, geometric curves on the dual of the lattice to study the spontaneous symmetry breaking.

It is known that the one-dimensional nearest-neighbor ferromagnetic Ising model does not undergo a phase transition at any temperature. On the other hand, if we add a polynomially decaying long-range interaction given by for , the works by Dyson and Fr\”{o}hlich-Spencer show the phase transition at low temperatures for . Moreover, Fr\”{o}hlich and Spencer defined a notion of contours for . There are many other works that study and extend the notion of contours for other .
%The work by Cassandro, Ferrari, Merola, and Presutti defined the contours for a region of

In this talk, we define a notion of contours for -dimensional long-range Ising model with , where the interactions are given by where and . As an application, we add non-homogeneous external fields in the Hamiltonian and give conditions for and so that the model undergoes a phase transition at low temperatures.

Date: Jul 03, 2024 at 16:15:00 h
Venue: Sala Multimedia CMM piso 6, Torre Norte, Beauchef 851.
Speaker: Eric Endo
Affiliation: NYU-Shanghai, China
Coordinator: Avelio Sepúlveda
More info at:
Event website
Abstract:
PDF

Posted on Jul 1, 2024 in Seminario de Probabilidades de Chile, Seminars