When topology triggers a phase transition

Michael Kastner

Physica A: Statistical Mechanics and its Applications, 2006, vol. 365, issue 1, 128-131

Abstract: 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 a such 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.

Keywords: Phase transition; Topology; Entropy; Analyticity; Long-range interaction (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:365:y:2006:i:1:p:128-131

DOI: 10.1016/j.physa.2006.01.036

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