Topology and phase transitions: paradigmatic evidence |
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Authors: | Franzosi Pettini Spinelli |
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Institution: | Dipartimento di Fisica, Universita di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy and Istituto Nazionale di Fisica della Materia, Unita di Firenze, Firenze, Italy. |
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Abstract: | We report upon the numerical computation of the Euler characteristic chi (a topologic invariant) of the equipotential hypersurfaces Sigma(v) of the configuration space of the two-dimensional lattice varphi(4) model. The pattern chi(Sigma(v)) versus v (potential energy) reveals that a major topology change in the family Sigma(v)(vinR) 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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