Critical phenomena and functional renormalization group

Shi YIN; Yangyang TAN; Weijie FU

doi:10.11889/j.0253-3219.2023.hjs.46.040002

Journals >NUCLEAR TECHNIQUES >Volume 46 >Issue 4 >Page 040002 > Article

NUCLEAR TECHNIQUES
Vol. 46, Issue 4, 040002 (2023)

Critical phenomena and functional renormalization group

Shi YIN, Yangyang TAN, and Weijie FU^*

Author Affiliations

School of Physics, Dalian University of Technology, Dalian 116024, China

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DOI: 10.11889/j.0253-3219.2023.hjs.46.040002 Cite this Article

Shi YIN, Yangyang TAN, Weijie FU. Critical phenomena and functional renormalization group[J]. NUCLEAR TECHNIQUES, 2023, 46(4): 040002 Copy Citation Text

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Fig. 1. Schematic phase diagram of QCD

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Flow diagram of RG equations around the Gaussian fixed point in dimensions (a) d>4, (b)2<d<4

Fig. 2. Flow diagram of RG equations around the Gaussian fixed point in dimensions (a)

d > 4

, (b)

2 < d < 4

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Fig. 3. (a) Flow diagram of RG equations around the W-F fixed point in

2 < d < 4

, (b) critical exponent

ν

in the order of

O (ε)

at the W-F fixed point obtained in the plane of

N

of the

O (N)

symmetry and the dimension

d

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Fig. 4. Critical exponent

ν

in the limit of large

N \to \infty

as a function of the spatial dimension

d

calculated with different values of the expansition order

n_{t r u n c}

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Fig. 5. 2D plot of the critical exponent

ν

as functions of the spatial dimension

d

and the symmetry

N

calculated with different values of the expansition order

n_{t r u n c}

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Fig. 6. Exact results of the critical exponent

ν

as functions of the spatial dimension

d

and the symmetry

N

with the truncation LPA

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Fig. 7.

R_{42}^{B} = χ_{4}^{B} / χ_{2}^{B}

R_{62}^{B} = χ_{6}^{B} / χ_{2}^{B}

and

R_{82}^{B} = χ_{8}^{B} / χ_{2}^{B}

as functions of the temperature at vanishing baryon chemical potential (

μ_{B} = 0

) in comparison with lattice results^[92]

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Fig. 8.

R_{42}^{B}

R_{62}^{B}

and

R_{82}^{B}

as functions of the temperature with different values of

μ_{B}

in the range of

0 ~ 400

MeV^[92]

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Fig. 9. Chemical freeze-out temperature and baryon chemical potential in the

T - μ_{B}

plane. The blue pentagons and red circles show the freeze-out data from Andronic et al and STAR experiment, respectively^[92]

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Fig. 10. Baryon number fluctuations

R_{42}^{B}

in the

T - μ_{B}

plane as well as the freeze-out curve: STAR Fit II^[92]

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Fig. 11. Baryon number fluctuations

R_{42}^{B}

R_{62}^{B}

and

R_{82}^{B}

as functions of the collision energy obtained in QCD-assisted LEFT in comparison to the STAR data^[92]

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Shi YIN, Yangyang TAN, Weijie FU. Critical phenomena and functional renormalization group[J]. NUCLEAR TECHNIQUES, 2023, 46(4): 040002

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