Topology and phase transitions: a paradigmatic evidence

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 ${\varphi }^4$ 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.

4 pages, 4 figures

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