Critical point signatures in the cluster expansion in fugacities
Abstract
The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase transition and a critical point at finite baryon density, in which the Fourier coefficients of the expansion can be determined explicitly and to arbitrary order. The asymptotic behavior of Fourier coefficients changes qualitatively as one traverses the critical temperature and it is connected to the branch points of a thermodynamic potential associated with the phase transition. The results are discussed in the context of lattice QCD simulations at imaginary chemical potential. We argue that the location of a branch point closest to the imaginary chemical potential axis can be extracted through an analysis of an exponential suppression of Fourier coefficients. This is illustrated using the four leading coefficients both in a toy model as well as by using recent lattice QCD data.
 Authors:

 Geothe Univ., Frankfort (Germany) ; Frankfurt Inst. for Advanced Studies (Germany)
 Geothe Univ., Frankfort (Germany)
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Geothe Univ., Frankfort (Germany) ; Frankfurt Inst. for Advanced Studies (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt (Germany)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 OSTI Identifier:
 1593193
 Alternate Identifier(s):
 OSTI ID: 1603605
 Grant/Contract Number:
 AC0205CH11231
 Resource Type:
 Published Article
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 1; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; critical phenomena; equations of state; lattice QCD; nuclear matter; phase diagrams; phase transitions; QCD phase transitions; thermodynamics; mean field theory; meanfield & cluster methods; statistical methods; thermal & statistical models
Citation Formats
Vovchenko, Volodymyr, Greiner, Carsten, Koch, Volker, and Stoecker, Horst. Critical point signatures in the cluster expansion in fugacities. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.014015.
Vovchenko, Volodymyr, Greiner, Carsten, Koch, Volker, & Stoecker, Horst. Critical point signatures in the cluster expansion in fugacities. United States. https://doi.org/10.1103/PhysRevD.101.014015
Vovchenko, Volodymyr, Greiner, Carsten, Koch, Volker, and Stoecker, Horst. Wed .
"Critical point signatures in the cluster expansion in fugacities". United States. https://doi.org/10.1103/PhysRevD.101.014015.
@article{osti_1593193,
title = {Critical point signatures in the cluster expansion in fugacities},
author = {Vovchenko, Volodymyr and Greiner, Carsten and Koch, Volker and Stoecker, Horst},
abstractNote = {The QCD baryon number density can formally be expanded into a Laurent series in fugacity, which is a relativistic generalization of Mayer's cluster expansion. We determine properties of the cluster expansion in a model with a phase transition and a critical point at finite baryon density, in which the Fourier coefficients of the expansion can be determined explicitly and to arbitrary order. The asymptotic behavior of Fourier coefficients changes qualitatively as one traverses the critical temperature and it is connected to the branch points of a thermodynamic potential associated with the phase transition. The results are discussed in the context of lattice QCD simulations at imaginary chemical potential. We argue that the location of a branch point closest to the imaginary chemical potential axis can be extracted through an analysis of an exponential suppression of Fourier coefficients. This is illustrated using the four leading coefficients both in a toy model as well as by using recent lattice QCD data.},
doi = {10.1103/PhysRevD.101.014015},
journal = {Physical Review D},
number = 1,
volume = 101,
place = {United States},
year = {2020},
month = {1}
}
https://doi.org/10.1103/PhysRevD.101.014015
Web of Science
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