Built on

M. Serone, G. Spada, and G. Villadoro, “ λ ϕ 2 4 \lambda\phi_{2}^{4} theory — Part II. the broken phase beyond NNNN(NNNN)LO,” JHEP
Original
1901
Earlier work this paper cites.
M. S. Pradeep and M. Stephanov, “Universality of the critical point mapping between Ising model and QCD at small quark mass,” Phys. Rev. D
Original
1905
Earlier work this paper cites.
A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, “Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan,” Phys. Rept
Original
1906
Earlier work this paper cites.
S. Mukherjee and V. Skokov, “Universality driven analytic structure of the QCD crossover: radius of convergence in the baryon chemical potential,” Phys. Rev. D
Original
1909
Earlier work this paper cites.
C.-N. Yang and T. D. Lee, “Statistical theory of equations of state and phase transitions. 1. Theory of condensation,” Phys. Rev
1952
Earlier work this paper cites.
T. D. Lee and C.-N. Yang, “Statistical theory of equations of state and phase transitions. 2. Lattice gas and Ising model,” Phys. Rev
1952
Earlier work this paper cites.
M. E. Fisher, “Critical point phenomena - the role of series expansions,” Rocky Mountain Journal of Mathematics
1974
Earlier work this paper cites.
D. J. Gross and A. Neveu, “Dynamical Symmetry Breaking in Asymptotically Free Field Theories,” Phys. Rev. D
1974
Earlier work this paper cites.
M. E. Fisher, “Yang-Lee Edge Singularity and phi**3 Field Theory,” Phys. Rev. Lett
1978
Earlier work this paper cites.
A. Chodos and H. Minakata, “The Gross-Neveu model as an effective theory for polyacetylene,” Phys. Lett. A
1994
Earlier work this paper cites.
M. Halasz, A. Jackson, and J. Verbaarschot, “Yang-lee zeros of a random matrix model for qcd at finite density,” Physics Letters B
1997
Earlier work this paper cites.

Similar

R. Guida and J. Zinn-Justin, “Critical exponents of the N vector model,” J. Phys. A
1998
Cited alongside, same era.
J. Zinn-Justin, “Quantum field theory and critical phenomena,” Int. Ser. Monogr. Phys
2002
Cited alongside, same era.
M. A. Stephanov, “QCD phase diagram and the critical point,” Prog. Theor. Phys. Suppl
2004
Cited alongside, same era.
A. Connelly, G. Johnson, S. Mukherjee, and V. Skokov, “Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point,” Nucl. Phys. A
Original
2004
Cited alongside, same era.
O. Schnetz, M. Thies, and K. Urlichs, “Phase diagram of the Gross-Neveu model: Exact results and condensed matter precursors,” Annals Phys
2004
Cited alongside, same era.

Then

X.-J. Liu, “Virial expansion for a strongly correlated fermi system and its application to ultracold atomic fermi gases,” Physics Reports
2012
Later among the works it cites.
X. An, D. Mesterházy, and M. A. Stephanov, “Functional renormalization group approach to the Yang-Lee edge singularity,” JHEP
Original
2016
Later among the works it cites.
C. Ratti, “Lattice QCD and heavy ion collisions: a review of recent progress,” Rept. Prog. Phys
Original
2018
Later among the works it cites.
X. An, D. Mesterházy, and M. A. Stephanov, “On spinodal points and Lee-Yang edge singularities,” J. Stat. Mech
Original
2018
Later among the works it cites.
X. An, D. Mesterhazy, and M. A. Stephanov, “Critical fluctuations and complex spinodal points,” PoS
2018

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2021

Universality, Lee-Yang singularities and series expansions

Basar, Gokce

Understand

We introduce a new way of reconstructing the equation of state of a thermodynamic system near a second order critical point from a finite set of Taylor coefficients computed away from the critical point.

We focus on the Ising universality class (${\mathbb Z}_2$ symmetry) and show that in the crossover region of the phase diagram it is possible to efficiently extract the location of the nearest thermodynamic singularity, the Lee-Yang edge singularity, from which one can (i) determine the location of the critical point, (ii) constrain the non-universal parameters that maps the equation of state to that of the Ising model in the scaling regime, and (iii) numerically evaluate the equation of state in the vicinity of the critical point.
This is done by using a combination of Pad\'e resummation and conformal maps.
We explicitly demonstrate these ideas in the celebrated Gross-Neveu model.

Built on

M. Serone, G. Spada, and G. Villadoro, “ λ ϕ 2 4 \lambda\phi_{2}^{4} theory — Part II. the broken phase beyond NNNN(NNNN)LO,” JHEP
Original
1901
Earlier work this paper cites.
M. S. Pradeep and M. Stephanov, “Universality of the critical point mapping between Ising model and QCD at small quark mass,” Phys. Rev. D
Original
1905
Earlier work this paper cites.
A. Bzdak, S. Esumi, V. Koch, J. Liao, M. Stephanov, and N. Xu, “Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan,” Phys. Rept
Original
1906
Earlier work this paper cites.
S. Mukherjee and V. Skokov, “Universality driven analytic structure of the QCD crossover: radius of convergence in the baryon chemical potential,” Phys. Rev. D
Original
1909
Earlier work this paper cites.
C.-N. Yang and T. D. Lee, “Statistical theory of equations of state and phase transitions. 1. Theory of condensation,” Phys. Rev
1952
Earlier work this paper cites.
T. D. Lee and C.-N. Yang, “Statistical theory of equations of state and phase transitions. 2. Lattice gas and Ising model,” Phys. Rev
1952
Earlier work this paper cites.
M. E. Fisher, “Critical point phenomena - the role of series expansions,” Rocky Mountain Journal of Mathematics
1974
Earlier work this paper cites.
D. J. Gross and A. Neveu, “Dynamical Symmetry Breaking in Asymptotically Free Field Theories,” Phys. Rev. D
1974
Earlier work this paper cites.
M. E. Fisher, “Yang-Lee Edge Singularity and phi**3 Field Theory,” Phys. Rev. Lett
1978
Earlier work this paper cites.
A. Chodos and H. Minakata, “The Gross-Neveu model as an effective theory for polyacetylene,” Phys. Lett. A
1994
Earlier work this paper cites.
M. Halasz, A. Jackson, and J. Verbaarschot, “Yang-lee zeros of a random matrix model for qcd at finite density,” Physics Letters B
1997
Earlier work this paper cites.

Similar

R. Guida and J. Zinn-Justin, “Critical exponents of the N vector model,” J. Phys. A
1998
Cited alongside, same era.
J. Zinn-Justin, “Quantum field theory and critical phenomena,” Int. Ser. Monogr. Phys
2002
Cited alongside, same era.
M. A. Stephanov, “QCD phase diagram and the critical point,” Prog. Theor. Phys. Suppl
2004
Cited alongside, same era.
A. Connelly, G. Johnson, S. Mukherjee, and V. Skokov, “Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point,” Nucl. Phys. A
Original
2004
Cited alongside, same era.
O. Schnetz, M. Thies, and K. Urlichs, “Phase diagram of the Gross-Neveu model: Exact results and condensed matter precursors,” Annals Phys
2004
Cited alongside, same era.

Then

X.-J. Liu, “Virial expansion for a strongly correlated fermi system and its application to ultracold atomic fermi gases,” Physics Reports
2012
Later among the works it cites.
X. An, D. Mesterházy, and M. A. Stephanov, “Functional renormalization group approach to the Yang-Lee edge singularity,” JHEP
Original
2016
Later among the works it cites.
C. Ratti, “Lattice QCD and heavy ion collisions: a review of recent progress,” Rept. Prog. Phys
Original
2018
Later among the works it cites.
X. An, D. Mesterházy, and M. A. Stephanov, “On spinodal points and Lee-Yang edge singularities,” J. Stat. Mech
Original
2018
Later among the works it cites.
X. An, D. Mesterhazy, and M. A. Stephanov, “Critical fluctuations and complex spinodal points,” PoS
2018

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

A. Connelly, G. Johnson, F. Rennecke, and V. Skokov, “Universal Location of the Yang-Lee Edge Singularity in O ⁡ ( N ) O(N) Theories,” Phys. Rev. Lett

Original

2006

Cited alongside, same era.

S. Ejiri, “Lee-Yang zero analysis for the study of QCD phase structure,” Phys. Rev. D

2006

Cited alongside, same era.

M. A. Stephanov, “QCD critical point and complex chemical potential singularities,” Phys. Rev. D

2006

Cited alongside, same era.

O. Schnetz, M. Thies, and K. Urlichs, “Full phase diagram of the massive Gross-Neveu model,” Annals Phys

2006

Cited alongside, same era.

O. Costin and G. V. Dunne, “Uniformization and Constructive Analytic Continuation of Taylor Series,” arXiv:2009.01962 [math.CV]

Original

2009

Cited alongside, same era.

G. Basar, G. V. Dunne, and M. Thies, “Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL(2) model,” Phys. Rev. D

Original

2009

Cited alongside, same era.

P. Fonseca and A. Zamolodchikov, “Ising field theory in a magnetic field: Analytic properties of the free energy,” arXiv:hep-th/0112167

Cited in the paper.