Topological conditions for discrete symmetry breaking and phase transitions

Abstract

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here.

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Cited by in corpus (11)

• Phase transitions and configuration space topology
• On the mean-field spherical model
• Exploring the energy landscape of XY models
• Kinetic energy and microcanonical nonanalyticities in finite and infinite systems
• Topology of configuration space of the mean-field phi^4 model by Morse theory
• A simple topological model with continuous phase transition
• Necessary and sufficient conditions for ${\mathbb{Z}}_2$-symmetry-breaking phase transitions
• Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces
• General theory for discrete symmetry-breaking equilibrium states
• Phase transitions triggered by dumbbell equipotential hypersurfaces
• Simplified energy landscape of the ${\varphi }^4$ model and the phase transition