Topology and phase transitions: Paradigmatic evidence

Year: 2000

Authors: Franzosi R., Pettini M., Spinelli L.

Autors Affiliation: Dipartimento di Fisica, Università di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy; Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy; Ist. Naz. di Fisica della Materia, Unità di Firenze, Firenze, Italy; Centre de Physique Théorique, C.N.R.S., Luminy Case 907, F-13288 Marseille Cedex 9, France; INFM, Unità di Ricerca di Torino, Dipto. di Fisica del Politecnico, C. so Duca degli Abruzzi 24, 10129 Torino, Italy; INEN, Sezione di Firenze, Italy

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 phi(4) model. The pattern chi(Sigma(v)) versus v (potential energy) reveals that a major topology change in the family {Sigma(v)}(v is an element of 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.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 84 (13)      Pages from: 2774  to: 2777

KeyWords: Eiffeomorphism invariants; Euler characteristics; Partition functions; Topologic invariants, Functions; Hamiltonians; Phase transitions; Potential energy; Theorem proving; Thermodynamics; Topology; Vectors, Polymers
DOI: 10.1103/PhysRevLett.84.2774

Citations: 57
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