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Topological aspects of geometrical signatures of phase transitions

Roberto Franzosi·Lapo Casetti·Lionel Spinelli·Marco Pettini
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Abstract

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.

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Roberto Franzosi, Lapo Casetti, Lionel Spinelli, Marco Pettini. 1998-10-15. Topological aspects of geometrical signatures of phase transitions. https://doi.org/10.1103/physreve.60.r5009

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