Universality of the critical point mapping between Ising model and QCD at small quark mass

Pradeep, Maneesha Sushama; Stephanov, Mikhail

doi:10.1103/physrevd.100.056003

Title: Universality of the critical point mapping between Ising model and QCD at small quark mass

Abstract

The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature $$T$$ and baryon chemical potential $$μ$$ in QCD to Gibbs free energy as a function of reduced temperature $$r$$ and magnetic field $$h$$ in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass $$m_ q$$. In particular, the angle between the $r = 0$ and $h = 0$ lines in the $(μ, T)$ plane vanishes as $$m^{2/5}_q$$. We discuss possible phenomenological consequences of these findings.

Authors:

^[1]; Stephanov, Mikhail ^[1]

Univ. of Illinois, Chicago, IL (United States)

Publication Date:: Mon Sep 09 00:00:00 EDT 2019

Research Org.:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1609364

Alternate Identifier(s):: OSTI ID: 1560774

Grant/Contract Number:: FG02-01ER41195; FG0201ER41195

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Volume: 100; Journal Issue: 5; 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; QCD phase transitions; Random matrix theory; Renormalization group

Citation Formats


                    Pradeep, Maneesha Sushama, and Stephanov, Mikhail. Universality of the critical point mapping between Ising model and QCD at small quark mass.  United States: N. p., 2019. 
Web.  doi:10.1103/physrevd.100.056003.

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                    Pradeep, Maneesha Sushama, & Stephanov, Mikhail. Universality of the critical point mapping between Ising model and QCD at small quark mass.  United States.  https://doi.org/10.1103/physrevd.100.056003

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                    Pradeep, Maneesha Sushama, and Stephanov, Mikhail. Mon .  
"Universality of the critical point mapping between Ising model and QCD at small quark mass".  United States.  https://doi.org/10.1103/physrevd.100.056003.  https://www.osti.gov/servlets/purl/1609364.

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@article{osti_1609364,

  title        = {Universality of the critical point mapping between Ising model and QCD at small quark mass},

  author       = {Pradeep, Maneesha Sushama and Stephanov, Mikhail},

  abstractNote = {The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature $T$ and baryon chemical potential $μ$ in QCD to Gibbs free energy as a function of reduced temperature $r$ and magnetic field $h$ in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass $m_ q$. In particular, the angle between the $r = 0$ and $h = 0$ lines in the $(μ, T)$ plane vanishes as $m^{2/5}_q$. We discuss possible phenomenological consequences of these findings.},

  doi          = {10.1103/physrevd.100.056003},

  journal      = {Physical Review. D.},

  number       = 5,

  volume       = 100,

  place        = {United States},

  year         = {Mon Sep 09 00:00:00 EDT 2019},

  month        = {Mon Sep 09 00:00:00 EDT 2019}

}

Copy to clipboard

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Works referencing / citing this record:

Critical behavior of the bulk viscosity in QCD
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Martinez, M.; Schäfer, T.; Skokov, V.
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Title: Universality of the critical point mapping between Ising model and QCD at small quark mass

Abstract

Citation Formats

Universality, the QCD critical and tricritical point, and the quark number susceptibility journal, January 2003

The universality class of the electroweak theory journal, October 1998

Critical exponents from field theory journal, May 1980

On spinodal points and Lee-Yang edge singularities journal, March 2018

QCD Phase Diagram and the Critical Point journal, January 2004

Parametric models and the Ising equation of state at order epsilon 3 journal, October 1974

Ising exponents from the functional renormalization group journal, April 2011

Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model journal, August 1952

Hydrodynamical evolution near the QCD critical end point journal, April 2005

Critical phenomena and renormalization-group theory journal, October 2002

Equation of State in the Neighborhood of the Critical Point journal, December 1965

Static and dynamic critical phenomena at a second order QCD phase transition journal, July 1993

Qcd Phase Diagram and the Critical Point journal, July 2005

Yang-Lee Edge Singularity and ϕ 3 Field Theory journal, June 1978

Critical exponents of the N -vector model journal, October 1998

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

Thermodynamics of strong-interaction matter from lattice QCD journal, October 2015

Subleading critical exponents from the renormalisation group journal, February 2004

The chiral critical point in 3-flavour QCD journal, March 2002

Critical exponents by the scaling-field method: The isotropic N -vector model in three dimensions journal, December 1984

Energy Dependence of Moments of Net-Proton Multiplicity Distributions at RHIC journal, January 2014

Revised Scaling Equation of State at the Liquid-Vapor Critical Point journal, July 1973

Phase diagram of QCD journal, September 1998

Tricritical scaling and renormalisation of ϕ 6 operators in scalar systems near four dimensions journal, June 1979

The chiral critical point in 3-flavour QCD journal, November 2001

Critical phenomena of fluids: Asymmetric Landau-Ginzburg-Wilson model journal, October 1981

Feynman-Graph Expansion for the Equation of State near the Critical Point (Ising-like Case) journal, August 1972

Signatures of the Tricritical Point in QCD journal, November 1998

Ising exponents from the functional renormalisation group text, January 2010

Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC text, January 2013

Critical Exponents of the N-vector model text, January 1998

The Chiral Critical Point in 3-Flavour QCD text, January 2001

QCD phase diagram and the critical point text, January 2004

Signatures of the Tricritical Point in QCD text, January 1998

Hydrodynamical evolution near the QCD critical end point text, January 2004

On spinodal points and Lee-Yang edge singularities text, January 2018

Equation of State in the Neighborhood of the Critical Point journal, December 1965

QCD and the chiral critical point journal, April 1994

Ising exponents from the functional renormalisation group text, January 2010

The Chiral Critical Point in 3-Flavour QCD text, January 2001

The universality class of the electroweak theory text, January 1998

QCD phase diagram and the critical point text, January 2004

Critical behavior of the bulk viscosity in QCD journal, October 2019

Universality, the QCD critical and tricritical point, and the quark number susceptibility
journal, January 2003

The universality class of the electroweak theory
journal, October 1998

Critical exponents from field theory
journal, May 1980

On spinodal points and Lee-Yang edge singularities
journal, March 2018

QCD Phase Diagram and the Critical Point
journal, January 2004

Parametric models and the Ising equation of state at order epsilon ³
journal, October 1974

Ising exponents from the functional renormalization group
journal, April 2011

Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
journal, August 1952

Hydrodynamical evolution near the QCD critical end point
journal, April 2005

Critical phenomena and renormalization-group theory
journal, October 2002

Equation of State in the Neighborhood of the Critical Point
journal, December 1965

Static and dynamic critical phenomena at a second order QCD phase transition
journal, July 1993

Qcd Phase Diagram and the Critical Point
journal, July 2005

Yang-Lee Edge Singularity and $ϕ^{3}$ Field Theory
journal, June 1978

Critical exponents of the N -vector model
journal, October 1998

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

Thermodynamics of strong-interaction matter from lattice QCD
journal, October 2015

Subleading critical exponents from the renormalisation group
journal, February 2004

The chiral critical point in 3-flavour QCD
journal, March 2002

Critical exponents by the scaling-field method: The isotropic $N$ -vector model in three dimensions
journal, December 1984

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Revised Scaling Equation of State at the Liquid-Vapor Critical Point
journal, July 1973

Phase diagram of QCD
journal, September 1998

Tricritical scaling and renormalisation of ϕ ⁶ operators in scalar systems near four dimensions
journal, June 1979

The chiral critical point in 3-flavour QCD
journal, November 2001

Critical phenomena of fluids: Asymmetric Landau-Ginzburg-Wilson model
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Feynman-Graph Expansion for the Equation of State near the Critical Point (Ising-like Case)
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Signatures of the Tricritical Point in QCD
journal, November 1998

Ising exponents from the functional renormalisation group
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Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC
text, January 2013

Critical Exponents of the N-vector model
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The Chiral Critical Point in 3-Flavour QCD
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QCD phase diagram and the critical point
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Signatures of the Tricritical Point in QCD
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Hydrodynamical evolution near the QCD critical end point
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On spinodal points and Lee-Yang edge singularities
text, January 2018

Equation of State in the Neighborhood of the Critical Point
journal, December 1965

QCD and the chiral critical point
journal, April 1994

Ising exponents from the functional renormalisation group
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QCD phase diagram and the critical point
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Critical behavior of the bulk viscosity in QCD
journal, October 2019