Critical point signatures in the cluster expansion in fugacities

Vovchenko, Volodymyr; Greiner, Carsten; Koch, Volker; Stoecker, Horst

doi:10.1103/PhysRevD.101.014015

Title: 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:

; Greiner, Carsten;

; Stoecker, Horst

Publication Date:: 2020-01-22

Research Org.:: Lawrence Berkeley National Lab. (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:: AC02-05CH11231

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 1; Journal ID: ISSN 2470-0010

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; mean-field & 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.

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                    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

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                    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.

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@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}

}

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Title: Critical point signatures in the cluster expansion in fugacities

Abstract

Citation Formats

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II journal, October 1961

Yang-Lee Distribution of Zeros for a van der Waals Gas journal, February 1964

Equations of state for real gases on the nuclear scale journal, July 2017

NJL-model analysis of dense quark matter journal, February 2005

Phase boundary for the chiral transition in ( 2 + 1 )-flavor QCD at small values of the chemical potential journal, January 2011

Search for Critical Behaviour of Strongly Interacting Matter at the CERN Super Proton Synchrotron journal, January 2016

QCD thermal phase transition in the presence of a small chemical potential journal, October 2002

Finite density QCD via an imaginary chemical potential journal, January 2003

Fourier coefficients of the net baryon number density and their scaling properties near a phase transition journal, June 2019

Net-baryon multiplicity distribution consistent with lattice QCD journal, February 2019

Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature journal, January 1999

New approach to canonical partition functions computation in N f = 2 lattice QCD at finite baryon density journal, May 2017

Dynamical symmetry breaking in asymptotically free field theories journal, November 1974

The four-Fermi model in three dimensions at non-zero density and temperature journal, February 1993

Thermal properties of interacting hadrons journal, September 1992

STANDING WAVE GROUND STATE IN HIGH DENSITY, ZERO TEMPERATURE QCD AT LARGE N C journal, February 1992

QCD at finite chemical potential with six time slices journal, December 2008

QCD equation of state to O ( μ B 6 ) from lattice QCD journal, March 2017

van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD journal, May 2017

Analytic structure of thermodynamic systems with repulsive interactions journal, December 2019

Chiral symmetry and density waves in quark matter journal, June 2005

Fourier coefficients of the net baryon number density and chiral criticality journal, July 2019

Remarks on the chiral phase transition in chromodynamics journal, January 1984

Third Moments of Conserved Charges as Probes of QCD Phase Structure journal, December 2009

Gauge theories with imaginary chemical potential and the phases of QCD journal, December 1986

The QCD phase diagram for small densities from imaginary chemical potential journal, October 2002

Asymptotic analysis of the Hermite polynomials from their differential–difference equation journal, December 2007

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I journal, April 1961

Large proton cumulants from the superposition of ordinary multiplicity distributions journal, November 2018

Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview journal, July 2017

Determination of the coexistence curve, critical temperature, density, and pressure of bulk nuclear matter from fragment emission data journal, May 2013

Trying to constrain the location of the QCD critical endpoint with lattice simulations journal, February 2019

Lattice-based QCD equation of state at finite baryon density: Cluster Expansion Model journal, February 2019

QCD critical point and complex chemical potential singularities journal, May 2006

QCD phenomenology based on a chiral effective Lagrangian journal, October 1994

QCD at zero baryon density and the Polyakov loop paradox journal, June 2006

On finite-density QCD at large Nc journal, May 2000

How to get from imaginary to real chemical potential journal, January 2007

Non-Gaussian Fluctuations near the QCD Critical Point journal, January 2009

Roberge-Weiss endpoint at the physical point of N f = 2 + 1 QCD journal, April 2016

The QCD equation of state at finite density from analytical continuation journal, November 2017

Cluster expansion model for QCD baryon number fluctuations: No phase transition at μ B / T < π journal, June 2018

Phase diagram of QCD journal, September 1998

The order of the quantum chromodynamics transition predicted by the standard model of particle physics journal, October 2006

Particle number fluctuations for the van der Waals equation of state journal, July 2015

Signatures of the Tricritical Point in QCD journal, November 1998

Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential journal, December 2017

Non-Gaussian particle number fluctuations in vicinity of the critical point for van der Waals equation of state journal, December 2015

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II
journal, October 1961

Yang-Lee Distribution of Zeros for a van der Waals Gas
journal, February 1964

Equations of state for real gases on the nuclear scale
journal, July 2017

NJL-model analysis of dense quark matter
journal, February 2005

Phase boundary for the chiral transition in ( $2 + 1$ )-flavor QCD at small values of the chemical potential
journal, January 2011

Search for Critical Behaviour of Strongly Interacting Matter at the CERN Super Proton Synchrotron
journal, January 2016

QCD thermal phase transition in the presence of a small chemical potential
journal, October 2002

Finite density QCD via an imaginary chemical potential
journal, January 2003

Fourier coefficients of the net baryon number density and their scaling properties near a phase transition
journal, June 2019

Net-baryon multiplicity distribution consistent with lattice QCD
journal, February 2019

Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature
journal, January 1999

New approach to canonical partition functions computation in N f = 2 lattice QCD at finite baryon density
journal, May 2017

Dynamical symmetry breaking in asymptotically free field theories
journal, November 1974

The four-Fermi model in three dimensions at non-zero density and temperature
journal, February 1993

Thermal properties of interacting hadrons
journal, September 1992

STANDING WAVE GROUND STATE IN HIGH DENSITY, ZERO TEMPERATURE QCD AT LARGE N _C
journal, February 1992

QCD at finite chemical potential with six time slices
journal, December 2008

QCD equation of state to $O (μ_{B}^{6})$ from lattice QCD
journal, March 2017

van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD
journal, May 2017

Analytic structure of thermodynamic systems with repulsive interactions
journal, December 2019

Chiral symmetry and density waves in quark matter
journal, June 2005

Fourier coefficients of the net baryon number density and chiral criticality
journal, July 2019

Remarks on the chiral phase transition in chromodynamics
journal, January 1984

Third Moments of Conserved Charges as Probes of QCD Phase Structure
journal, December 2009

Gauge theories with imaginary chemical potential and the phases of QCD
journal, December 1986

The QCD phase diagram for small densities from imaginary chemical potential
journal, October 2002

Asymptotic analysis of the Hermite polynomials from their differential–difference equation
journal, December 2007

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I
journal, April 1961

Large proton cumulants from the superposition of ordinary multiplicity distributions
journal, November 2018

Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview
journal, July 2017

Determination of the coexistence curve, critical temperature, density, and pressure of bulk nuclear matter from fragment emission data
journal, May 2013

Trying to constrain the location of the QCD critical endpoint with lattice simulations
journal, February 2019

Lattice-based QCD equation of state at finite baryon density: Cluster Expansion Model
journal, February 2019

QCD critical point and complex chemical potential singularities
journal, May 2006

QCD phenomenology based on a chiral effective Lagrangian
journal, October 1994

QCD at zero baryon density and the Polyakov loop paradox
journal, June 2006

On finite-density QCD at large Nc
journal, May 2000

How to get from imaginary to real chemical potential
journal, January 2007

Non-Gaussian Fluctuations near the QCD Critical Point
journal, January 2009

Roberge-Weiss endpoint at the physical point of $N_{f} = 2 + 1$ QCD
journal, April 2016

The QCD equation of state at finite density from analytical continuation
journal, November 2017

Cluster expansion model for QCD baryon number fluctuations: No phase transition at $μ_{B} / T < π$
journal, June 2018

Phase diagram of QCD
journal, September 1998

The order of the quantum chromodynamics transition predicted by the standard model of particle physics
journal, October 2006

Particle number fluctuations for the van der Waals equation of state
journal, July 2015

Signatures of the Tricritical Point in QCD
journal, November 1998

Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential
journal, December 2017

Non-Gaussian particle number fluctuations in vicinity of the critical point for van der Waals equation of state
journal, December 2015