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