Journal Article

FZJ-2022-02387

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The geometric theory of phase transitions

Di Cairano, L. (Corresponding author)FZJ*

2022
IOP Publ. Bristol

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Please use a persistent id in citations: http://hdl.handle.net/2128/31868  doi:10.1088/1751-8121/ac717d

Abstract: We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. Such a theory allows to rephrase the Bachmann's classification of PTs for finite-size systems in terms of geometric properties of the energy level sets (ELSs) associated to the Hamiltonian function. Specifically, by defining the microcanonical entropy as the logarithm of the ELS's volume equipped with a suitable metric tensor, we obtain an exact equivalence between thermodynamics and geometry. In fact, we show that any energy-derivative of the entropy can be associated to a specific combination of geometric curvature structures of the ELSs which, in turn, are well-precise combinations of the potential function derivatives. In so doing, we establish a direct connection between the microscopic description provided by the Hamiltonian and the collective behavior which emerges in a PT. Finally, we also analyze the behavior of the ELSs' geometry in the thermodynamic limit showing that nonanalyticities of the energy-derivatives of the entropy are caused by nonanalyticities of certain geometric properties of the ELSs around the transition point. We validate the theory studying PTs that occur in the ϕ4 and Ginzburg–Landau-like models.

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Contributing Institute(s):

1. Computational Biomedicine (IAS-5)
2. Computational Biomedicine (INM-9)

Research Program(s):

1. 899 - ohne Topic (POF4-899) (POF4-899)

Appears in the scientific report 2022

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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