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Microcanonical phase transitions for the vortex system

Dario Benedetto, Emanuele Caglioti and Margherita Nolasco

Vol. 12 (2024), No. 1, 85–112
Abstract

We consider the microcanonical variational principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of the second kind, i.e., for which the equivalence of ensembles does not hold.

For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit an arbitrary number of first-order phase transitions, while the entropy is convex for large energy.

Keywords
mean-field equation, microcanonical ensemble, vortex system, phase transitions
Mathematical Subject Classification
Primary: 35Q82, 82M30
Secondary: 35Q35, 82B26
Milestones
Received: 1 July 2023
Accepted: 2 November 2023
Published: 20 December 2023

Communicated by Raffaele Esposito
Authors
Dario Benedetto
Dipartimento di Matematica
Università di Roma “La Sapienza”
Rome
Italy
INdAM — Istituto Nazionale di Alta Matematica, GNFM
Rome
Italy
Emanuele Caglioti
Dipartimento di Matematica
Università di Roma “La Sapienza”
Rome
Italy
INdAM — Istituto Nazionale di Alta Matematica, GNFM
Rome
Italy
Margherita Nolasco
Dipartimento di Ingegneria e Scienze dell’informazione e Matematica
Università degli studi dell’Aquila
L’Aquila
Italy
INdAM — Istituto Nazionale di Alta Matematica, GNAMPA
Rome
Italy