Topology and phase transitions: a paradigmatic evidence
Roberto Franzosi, Marco Pettini, Lionel Spinelli
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) vs. v (potential energy) reveals that a major topology change in the family Σvv∈ 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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