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When topology triggers a phase transition

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  • Kastner, Michael

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.

Suggested Citation

  • Kastner, Michael, 2006. "When topology triggers a phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 128-131.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:128-131
    DOI: 10.1016/j.physa.2006.01.036
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