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arXiv · cond-mat/9911235

Topology and phase transitions: a paradigmatic evidence

Roberto Franzosi·Marco Pettini·Lionel Spinelli
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Abstract

We report upon the numerical computation of the Euler characteristic χ(a topologic invariant) of the equipotential hypersurfaces Σ_v of the configuration space of the two-dimensional lattice $ϕ^4$ model. The pattern χ(Σ_v) vs. v (potential energy) reveals that a major topology change in the family {Σ_v}_{v\in 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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Roberto Franzosi, Marco Pettini, Lionel Spinelli. 1999-11-16. Topology and phase transitions: a paradigmatic evidence. https://doi.org/10.1103/physrevlett.84.2774

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