Abstract
In a recent paper a toy model (hypercubic model) undergoing a first-order -symmetry-breaking phase transition (-SBPT) was introduced. The hypercubic model was inspired by the topological hypothesis, according to which a phase transition may be entailed by suitable topological changes of the equipotential surfaces (Σv’s) of configuration space. In this paper we show that at the origin of a -SBPT there is a geometric property of the Σv’s, i.e. dumbbell-shaped Σv’s suitably defined, which includes a topological change as a limiting case. This property is necessary and sufficient condition to entail a -SBPT. This new approach has been applied to three models: a modified version introduced here of the hypercubic model, a model introduced in a recent paper with a continuous -SBPT belonging to several universality classes, and finally to a physical models, i.e. the mean-field ϕ4 model and a simplified version of it.
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