Scientific Results

On the origin of phase transitions in the absence of symmetry-breaking

Year: 2019

Authors: Pettini G., Gori M., Franzosi R., Clementi C.,
Pettini M.

Autors Affiliation: Dipartimento di Fisica Università di Firenze, and I.N.F.N., Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy;
Centre de Physique Théorique, Aix-Marseille University, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France;
QSTAR & CNR – Istituto Nazionale di Ottica, Largo Enrico Fermi 2, I-50125 Firenze, Italy;
Department of Chemistry, Rice University, 6100 Main street, Houston, TX 77005-1892, USA;
Centre de Physique Théorique, Aix-Marseille University, Campus de Luminy, Case 907, 13288 Marseille Cedex 09, France;

Abstract: In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three
spatial dimensions. Our model Hamiltonian is defined on the basis of a continuum version
of a duality transformation of a three dimensional Ising model. The system so obtained
undergoes a thermodynamic phase transition in the absence of a global symmetry-breaking
and thus in the absence of an order parameter. It is found that the first order phase
transition undergone by this model fits into a microcanonical version of an Ehrenfest-like
classification of phase transitions applied to the configurational entropy. It is discussed why
the seemingly divergent behaviour of the third derivative of configurational entropy is the
effect of a deeper geometrical transition of the equipotential submanifolds of configuration
space, which, in its turn, is likely to be the “shadow” of an even deeper transition of
topological kind.

Journal/Review: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Volume: 516      Pages from: 376  to: 392

KeyWords: Microcanonical phase transitions; Topology and phase transitions; Hamiltonian dynamics and phase transitio
DOI: 10.1016/j.physa.2018.10.001

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English