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

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

2001-04-14

arxiv.org/abs/cond-mat/0104267v1

Phys. Rev. E 65, 036112 (2002)

Physics

Condensed Matter

Statistical Mechanics

REVTeX file, 5 pages, 1 PostScript figure

Scientific paper

10.1103/PhysRevE.65.036112

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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