The Dynamics of a Spin-Flip System by an Example: the Curie-Weiss Model

ARGOMENTI: Seminars Ph.D. Program

Wednesday 11 March 2009 h. 15:00, room 2AB/40
Francesca Collet (Ph.D. in Applied Math., Dip. Mat.)
"The Dynamics of a Spin-Flip System by an Example: the Curie-Weiss Model"

A spin system is a system composed by N sites at which is associated randomly a +1 or -1 value, called spin. Each spin is influenced by all the others in the same way and this makes it flip with a certain probability. The dynamics just mentioned are completely described by the time evolution of the Magnetization (the sum of all the spin values divided by N), so it is sufficient to study the behavior of this last quantity. As N grows to infinity, its limiting dynamics are deterministic (driven by ODE) and exhibit a phase transition: multiple equilibrium solutions arise depending on the value of a parameter, which is the inverse of the temperature. The Curie-Weiss model is a basic example of it.
After having recalled some notions of Probability, we try to explain in a simple and intuitive way, avoiding the most part of the technicalities, how the Curie-Weiss model evolves in time at different temperatures.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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