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SYEL: Symposium Energy Landscapes: Statistical Physics of (Spin-)Glasses, Biomolecules, Clusters and Optimization Problems

SYEL 1: Energy Landscapes: Statistical Physics of (Spin-)Glasses, Biomolecules, Clusters and Optimization Problems (SYEL)

SYEL 1.4: Hauptvortrag

Montag, 22. März 2010, 11:30–12:00, H1

Energy landscapes and phase transitions — •Lapo Casetti — Dipartimento di Fisica e Astronomia, Università di Firenze, and INFN, Firenze, Italy

Our current understanding of phase transitions in equilibrium statistical mechanics is remarkable. This notwithstanding, we still do not know which features of the Hamiltonian of a system induce a phase transition.

A natural framework for approaching this problem is energy landscape theory. The potential energy landscape of a classical system is the graph of the potential energy function V(q₁,…,q_N), where the q’s are the coordinates of configuration space. The role played by the stationary points of the landscape, where dV = 0, is crucial. Remarkably, these are the points where the topology of the level sets of V changes. It has been conjectured that some of these topology changes are related to thermodynamic phase transitions; it has also been shown that the stationary points of V are in one-to-one correspondence with the singularities of the microcanonical entropy at finite N.

Microcanonical singularities at finite N disappear in the thermodynamic limit unless the corresponding stationary points become asymptotically flat. This suggests that thermodynamic phase transitions may be induced by asymptotically flat stationary points of the energy landscape. We discuss some explicit examples of models of physical interest where this idea can be successfully tested.