Phase Transitions from Saddles of the Potential Energy Landscape

Abstract

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated.

5 pages, no figures

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Cited by in corpus (19)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Phase transitions and configuration space topology
• Excited-state quantum phase transitions
• Quantum quench influenced by an excited-state phase transition
• Phase transitions detached from stationary points of the energy landscape
• Energy landscape analysis of the two-dimensional nearest-neighbor ϕ^4 model
• Computational topology for configuration spaces of hard disks
• Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
• Phase transitions induced by saddle points of vanishing curvature
• Exploring the energy landscape of XY models
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
• Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
• Microcanonical phase diagrams of short-range ferromagnets
• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Potential Energy Landscape of the Two-Dimensional XY Model: Higher-Index Stationary Points
• A simple topological model with continuous phase transition
• Microcanonical entropy of the spherical model with nearest-neighbour interactions
• Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces
• Energy landscapes and their relation to thermodynamic phase transitions