Topology and phase transitions: a paradigmatic evidence
Abstract
We report upon the numerical computation of the Euler characteristic (a topologic invariant) of the equipotential hypersurfaces v of the configuration space of the two-dimensional lattice φ4 model. The pattern (v) vs. v (potential energy) reveals that a major topology change in the family vv∈ 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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