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Phase transitions as topology changes in configuration space: an exact result

Lapo Casetti·E. G. D. Cohen·Marco Pettini
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Abstract

The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.

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Lapo Casetti, E. G. D. Cohen, Marco Pettini. 2001-04-14. Phase transitions as topology changes in configuration space: an exact result. https://doi.org/10.1103/physreve.65.036112

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