Topology and Phase Transitions: Paradigmatic Evidence

Roberto Franzosi (1, 2) , Marco Pettini (3, 2) , Lionel Spinelli (4, 2)

1 Dipartimento di Fisica e Astronomia [Firenze]
2 Istituto Nazionale di Fisica della Materia
3 OAA - INAF - Osservatorio Astrofisico di Arcetri
4 CPT - Ex E8 Dynamique non linéaire

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) versus v (potential energy) reveals that a major topology change in the family {Σv}v∈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.

Domaines: Physique mathématique [math-ph]

Roberto Franzosi, Marco Pettini, Lionel Spinelli. Topology and Phase Transitions: Paradigmatic Evidence. 2023. ⟨hal-01431921⟩