The Ising model and its phase diagram
Event details
| Date | 22.04.2013 |
| Hour | 17:15 › 18:00 |
| Speaker | Ludovic Pirl (EPFL) |
| Location |
MA A3 30
|
| Category | Conferences - Seminars |
Hamiltonian Dynamics Seminar
In this talk, we will present the Ising Model. It's goal is to study the properties of an interacting system of spins taking value -1 or +1 on the grid Z^d. We will construct probability measures (Gibbs measures) on A = {-1,1}^{Z^d} as limit measures of measures on finite parts of A, which will encrypt the information we want to have at hand, namely: closest neighbour interactions, dependence on an exterior magnetic field and a given temperature. We will define magnetization and see how the existence of more than one infinite dimensional Gibbs measure (a so-called first order transition) at a specific magnetic field and temperature corresponds to a discontinuity in the magnetization as a function of the magnetic field. The goal will be to show a classification of all possible behaviours of the system as a function of the magnetic field, the temperature of the system, and the dimension of the grid.
In this talk, we will present the Ising Model. It's goal is to study the properties of an interacting system of spins taking value -1 or +1 on the grid Z^d. We will construct probability measures (Gibbs measures) on A = {-1,1}^{Z^d} as limit measures of measures on finite parts of A, which will encrypt the information we want to have at hand, namely: closest neighbour interactions, dependence on an exterior magnetic field and a given temperature. We will define magnetization and see how the existence of more than one infinite dimensional Gibbs measure (a so-called first order transition) at a specific magnetic field and temperature corresponds to a discontinuity in the magnetization as a function of the magnetic field. The goal will be to show a classification of all possible behaviours of the system as a function of the magnetic field, the temperature of the system, and the dimension of the grid.
Links
Practical information
- Informed public
- Free
Organizer
- Sonja Hohloch, Martins Bruveris