Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 2: Statistical physics I (general)

DY 2.7: Vortrag

Montag, 25. Februar 2008, 12:00–12:15, MA 001

Phase transitions from saddle points of the potential energy landscape — •Michael Kastner — Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth

The relation between saddle points of the potentials of classical many-particle systems and the analyticity properties of thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the entropy, and the functional form of this nonanalytic term can be derived explicitly. With increasing system size, the order of the nonanalytic term grows unboundedly, leading to an increasing differentiability of the entropy. Nonetheless, a distribution of an unboundedly growing number of saddle points may cause a phase transition in the thermodynamic limit. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, conditions on the distribution of saddle points and their curvatures are derived which are necessary for a phase transition to occur. For several spin models, the absence or presence of a phase transition is predicted from saddle points and their local curvatures in microscopic(!) configuration space.