Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 42: Critical Phenomena and Phase Transitions II
DY 42.3: Vortrag
Donnerstag, 30. März 2006, 11:30–11:45, H\"UL 186
When topology triggers a phase transition — •Michael Kastner — Physikalisches Institut, Lehrstuhl für Theoretische Physik, Universität Bayreuth, 95440 Bayreuth
Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by such a topology change are discussed. The first one is a model with long-range interactions, namely the mean-field ϕ4-model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermodynamic singularity is generated by a maximization over one variable (or one discrete index) of a smooth function, although the context in which the maximization occurs is very different.