Phase transitions induced by saddle points of vanishing curvature

Abstract

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.

5 pages

References in corpus (2)

• Phase transitions and configuration space topology
• Phase transitions and topology changes in configuration space

Cited by in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
• Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
• Energy landscapes and their relation to thermodynamic phase transitions