### Energy landscapes and their relation to thermodynamic phase transitions

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05/06/2008, 14:15, D5-153
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**
Michael Kastner, Lehrstuhl für Theoretische Physik, Bayreuth **

A phase transition is an abrupt change of the macroscopic properties
of a many-particle system under variation of a control parameter. An
approach commonly used for the theoretical description of phase
transitions is the investigation of the analyticity properties of
thermodynamic functions like the canonical free energy. While it is
long known that nonanalytic behavior in a canonical thermodynamic
function can occur only in the thermodynamic limit, it was recently
observed that the microcanonical entropy of a finite system is not
necessarily infinitely many times differentiable.

In order to better understand the occurrence of nonanalyticities of
thermodynamic functions, we adopt an approach based on the study of
energy landscapes: The relation between saddle points of the potential
energy landscape of a classical many-particle system and the
analyticity properties of its thermodynamic functions is studied. For
finite systems, each saddle point is found to cause a nonanalyticity
in the microcanonical 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, in the
thermodynamic limit, asymptotically flat saddle points may cause a
phase transition to take place. 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.

These results establish a relationship between properties of energy
landscapes and the occurrence of phase transitions. Such an approach
appears particularly promising for the simultaneous study of dynamical
and thermodynamical properties, as is of interest for example for
protein folding or the glass transition.