Scientific Results

Topological origin of phase transitions in the absence of critical points of the energy landscape

Year: 2018

Authors: Gori M., Franzosi R., Pettini M.

Autors Affiliation: Aix Marseille Univ, Université de Toulon, CNRS, CPT, 13288 Marseille, France;
QSTAR & CNR Istituto Nazionale di Ottica, Largo Enrico Fermi 2, 50125, Firenze, Italy;
Aix Marseille Univ, Université de Toulon, CNRS, CPT, 13288 Marseille, France

Abstract: Different arguments led us to surmise that the deep origin of phase transitions has to be identified with suitable topological changes of potential-related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of equipotential energy submanifolds of configuration space. However, it has been recently shown that the 2D lattice phi(4)-model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, also the phase transition of this model stems from a change of topology of both the energy and potential level sets. But in this case the topology changes are asymptotic (N -> infinity). This fact is not obvious since the Z(2) symmetry-breaking transition could be given measure-based explanations in presence of trivial topology.

Journal/Review: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Volume: 2018      Pages from: 093204-1  to: 093204-25

KeyWords: classical phase transitions; dynamical processes;
DOI: 10.1088/1742-5468/aad6b6

Citations: 2
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English