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

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

More Information: The authors acknowledge the financial support of the Future and Emerging Technologies (FET) Program within the Seventh Framework Program (FP7) for Research of the European Commission, under the FET-Proactive TOPDRIM Grant No. FP7-ICT-318121. The project leading to this publication has received funding also from the Excellence Initiative of Aix Marseille University – A*Midex, a French \”Investissements d\’Avenir\” programme. Roberto Franzosi thanks the support by the QuantERA projects Q-Clocks, Italy. Cecilia Clementi acknowledges support by the National Science Foundation, USA (CHE-1265929, CHE-1738990, and PHY-1427654), the Welch Foundation, USA (C-1570), and the Einstein Foundation in Berlin, Germany. Part of this work was done while M.P. was on leave of absence from Osservatorio Astrofisico di Arcetri, Florence, Italy.
KeyWords: Entropy; Hamiltonians; Ising model; Topology, Configuration space; Configurational entropy; Duality transformation; First-order phase transitions; Hamiltonian dynamics; Model Hamiltonians; Symmetry-breaking; Three-dimensional Ising model, Phase transitions
DOI: 10.1016/j.physa.2018.10.001

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