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Finite size scaling study of $N_{\text{f}}=4$ finite density QCD on the lattice
High Energy Physics - Lattice · Submitted 27 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our finite-size analyses show that the transition is first order at $(\beta, \kappa, \mu/T)=(1.58, 0.1385, 0.584\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.822, 0.154)$.
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The abstract, sentence by sentence
We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{\text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. The $\mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $\mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(\beta, \kappa, \mu/T)=(1.58, 0.1385, 0.584\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.822, 0.154)$. It weakens considerably at $(\beta, \kappa, \mu/T)=(1.60, 0.1371, 0.821\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. | contribution 0.95 | 0.95 | 0.02 | asserted 0.95 |
| s1 | In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. | method 0.96 | 0.95 | 0.03 | asserted 0.85 |
| s2 | Simulations were carried out on lattices of a temporal size fixed at $N_{\text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. | method 1.00 | 0.95 | 0.02 | asserted 0.99 |
| s3 | Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. | method 1.00 | 0.95 | 0.01 | asserted 1.00 |
| s4 | The $\mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. | method 1.00 | 0.91 | 0.03 | asserted 1.00 |
| s5 | Among various approximation schemes for calculating the ratio of quark determinants needed for $\mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. | method 0.78 | 0.96 | 0.03 | asserted 1.00 |
| s6 | Our finite-size analyses show that the transition is first order at $(\beta, \kappa, \mu/T)=(1.58, 0.1385, 0.584\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.822, 0.154)$. | result 1.00 | 0.97 | 0.78 | asserted 1.00 |
| s7 | It weakens considerably at $(\beta, \kappa, \mu/T)=(1.60, 0.1371, 0.821\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out. | result 0.93 | 0.94 | 0.16 | hedged possibility 0.85 |
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The paper
Original abstract
We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{\text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. The $\mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $\mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(\beta, \kappa, \mu/T)=(1.58, 0.1385, 0.584\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.822, 0.154)$. It weakens considerably at $(\beta, \kappa, \mu/T)=(1.60, 0.1371, 0.821\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out.
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References
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 2 papers
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Thus we adopt a cheaper approximation method, that is, the Taylor expansion of the logarithm of determinant which is known to have better convergence property than the other expansion schemes [ref] , ln( D(m_0^',μ^')/D(m_0,μ) ) = [ ∑_j,k=0^∞Δm_0^j Δμ^k/j!k!
Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD · Reweighting · 0.95
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We study the finite temperature and density ensembles generated with a phase-quenched fermion determinant [ref] , using four fermion flavors of the Wilson-clover action and the Iwasaki gauge action.
Zeros of QCD partition function from finite density lattices · Introduction · 0.80
Cites it as background 3 papers
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The phase structure of four-flavor QCD on the $T -$ plane has been investigated by various methods including the CLM using either staggered fermions [ref] or Wilson fermions [ref] .
Complex Langevin calculations in QCD at finite density · Introduction · 0.97
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The CPs in the light and heavy quark-mass regions have been investigated in lattice-QCD numerical simulations for decades [ref] .
High-precision analysis of the critical point in heavy-quark QCD at $N_t=6$ · Introduction · 0.94
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For instance, higher-order cumulants have been studied at zero chemical potential [ref] and at finite chemical potential [ref] .
Net baryon number fluctuations across the chiral phase transition at finite density in the strong coupling lattice QCD · Introduction · 0.97
What it cites · 15 sentences without a confident label
Uses the method or tool of 4 papers
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After reduction in the temporal direction, the quark determinant can be expressed as [equation] where the definition of $A_0$, $H_±$ and $H_0$ are given in Ref. [ref] .
On the phase of quark determinant in lattice QCD with finite chemical potential · Phase reweighting · 0.97
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In order to avoid introduction of systematic errors, we perform an exact calculation of the quark determinant by adopting the reduction technique of Ref. [ref] .
Winding expansion techniques for lattice QCD with chemical potential · Phase reweighting · 1.00
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The Omelyan integrator [ref] was adopted in our simulation.
Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD · Simulation parameters · 1.00
Compares with 1 paper
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We numerically compare the two approaches in Fig. [ref] for the same parameter set; filled symbols in (a) with vertical error bars are the canonical results from Fig. 7 (bottom) in Ref. [ref] , whereas open symbols in (b) with horizontal error bars are our grand canonical results.
Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method · Comparision with the Kentucky group · 0.90
Cites as background 1 paper
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The Kentucky group [ref] studied the phase structure of the 4-flavor theory using the canonical approach employing the Wilson-clover quark action.
Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method · Introduction · 0.97
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