Topological approach to phase transitions and inequivalence of statistical ensembles

Abstract

The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model with mean field-type interactions is considered. Exact results for microcanonical and canonical quantities are compared with topological properties of a certain family of submanifolds of the state space. Due to the observed ensemble inequivalence, a close relation is expected to exist only between the topological approach and one of the statistical ensembles. It is found that the observed topology changes can be interpreted meaningfully when compared to microcanonical quantities.

9 pages, 1 figure

References in corpus (3)

• Phase transitions and topology changes in configuration space
• Unattainability of a purely topological criterion for the existence of a phase transition for non-confining potentials
• On the mean-field spherical model

Cited by in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Phase transitions and configuration space topology
• The mean-field phi4-model: entropy, analyticity, and configuration space topology
• Continuous phase transitions with a convex dip in the microcanonical entropy
• On the mean-field spherical model
• Exploring the energy landscape of XY models
• Nonanalyticities of entropy functions of finite and infinite systems
• Topological Theory of Phase Transitions