Phase transitions induced by saddle points of vanishing curvature

Details Phase transitions induced by saddle points of vanishing curvature Phase transitions induced by saddle points of vanishing curvature

2007-11-06

arxiv.org/abs/0711.0852v2

Phys. Rev. Lett. 100, 160601 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

10.1103/PhysRevLett.100.160601

Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long standing question of which topology changes in configuration space can induce a phase transition.

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