SEMINAIRE MERCREDI 5 MARS 2008
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Michael Kastner
Physikalisches Institut
UniversitŠt Bayreuth
95440 Bayreuth
Germany

Title: Phase transitions induced by saddles of the potential energy landscape

Abstract: Saddle points of the potential energy function are known to
play an important role for dynamic as well as thermodynamic properties
of classical many-particle systems. In this talk, I present exact and
model-independent results on the relation of such saddle points to the
analyticity properties of thermodynamic functions for both, finite and
infinite systems. Remarkably, for finite systems each saddle point is
found to cause a nonanalyticity of the entropy, but the strength of
this nonanalyticity is weak in the limit of large system sizes.
Analyzing the contribution of the (very many) saddle points to the
entropy 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 can be predicted from saddle points and
their local curvatures in microscopic(!) configuration space.