Energy landscape and phase transitions in the self-gravitating ring model

Abstract

We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the self-gravitating ring model. We show analytically that the criterion correctly singles out the phase transition between a homogeneous and a clustered phase and also suggests the presence of another phase transition, not previously known. On the basis of the properties of the energy landscape we conjecture on the nature of the latter transition.

References in corpus (6)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Phase transitions and configuration space topology
• Phase transitions induced by saddle points of vanishing curvature
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
• Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
• Energy landscape properties studied by symbolic sequences

Cited by in corpus (17)

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• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Stationary point approach to the phase transition of the classical XY chain with power-law interactions
• Solvable model of a self-gravitating system
• Phase transitions in simplified models with long-range interactions
• Non existence of a phase transition for the Penetrable Square Wells in one dimension
• Ensemble Inequivalence and Maxwell Construction in the Self-Gravitating Ring Model
• Coarse-grained collisionless dynamics with long-range interactions
• Geometry of the energy landscape of the self-gravitating ring
• Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces
• Density of states of the $XY$ model: an energy landscape approach