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Topology and Phase Transitions: Paradigmatic Evidence

Abstract

We report upon the numerical computation of the Euler characteristic χ (a topologic invariant) of the equipotential hypersurfaces Σv of the configuration space of the two-dimensional lattice ϕ4 model. The pattern χ(Σv) versus v (potential energy) reveals that a major topology change in the family {Σv}v∈R is at the origin of the phase transition in the model considered. The direct evidence given here—of the relevance of topology for phase transitions—is obtained through a general method that can be applied to any other model.
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hal-01431921 , version 1 (13-09-2023)

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Roberto Franzosi, Marco Pettini, Lionel Spinelli. Topology and Phase Transitions: Paradigmatic Evidence. 2023. ⟨hal-01431921⟩
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