Topological origin of the phase transition in a mean-field model

Details Topological origin of the phase transition in a mean-field model Topological origin of the phase transition in a mean-field model

1998-10-30

arxiv.org/abs/cond-mat/9810406v2

Physical Review Letters 82, 4160 (1999).

Physics

Condensed Matter

Statistical Mechanics

REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.82.4160

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.

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