Topology of configuration space of the mean-field phi^4 model by Morse theory

Abstract

In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field ${\varphi }^4$ model with a ${\mathbb{Z}}_2$ symmetry. Our purpose is discovering, if any, the relation between the second-order ${\mathbb{Z}}_2$-symmetry breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results at the light of two theorems on sufficiency conditions for symmetry breaking phase transitions recently proven. This study makes part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.

arXiv comment11 pages, 10 figures

References in corpus (9)

• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Phase transitions and configuration space topology
• Phase transitions detached from stationary points of the energy landscape
• The mean-field phi4-model: entropy, analyticity, and configuration space topology
• Energy landscape analysis of the two-dimensional nearest-neighbor ϕ^4 model
• Topological origin of the phase transition in a mean-field model
• Phase transitions as topology changes in configuration space: an exact result
• Topological conditions for discrete symmetry breaking and phase transitions
• On the apparent failure of the topological theory of phase transitions

Cited by in corpus (4)

• Necessary and sufficient conditions for ${\mathbb{Z}}_2$-symmetry-breaking phase transitions
• Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces
• Phase transitions triggered by dumbbell equipotential hypersurfaces
• Simplified energy landscape of the ${\varphi }^4$ model and the phase transition