A theory of chaos in disordered systems |
Abstract: Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy function (Hamiltonian) is random. Examples include various models of spin glasses and polymers. They also arise in other disciplines, like fitness models in evolutionary biology. A disordered system is called chaotic if a small perturbation of the energy landscape causes a drastic change in some feature of the system, such as the ground state. In this talk I will present a series of basic new results about Gaussian random fields, that lead to a rigorous theory of chaos in disordered systems and confirms long-standing physics intuition about connections between chaos, anomalous fluctuations of the ground state energy, and the existence of multiple valleys in the energy landscape. As a specific application of the theory, (if time permits) I will sketch the resolution of the bond chaos conjecture for the Sherrington-Kirkpatrick model of spin glasses. |
Web page: Alexandru I. Suciu | Comments to: alexsuciu@neu.edu | |
Posted: May 5, 2010 | URL: http://www.math.neu.edu/bhmn/chatterjee10.html |