Fixed point behavior of cumulants in the three-dimensional Ising universality class

Abstract

High-order cumulants and factorial cumulants of conserved charges are suggested to study the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the three-dimensional Ising model which is believed to belong to the same universality class with the Quantum chromo-dynamics, temperature dependence of the second- to fourth-order (factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated by Monte Carlo method, the fixed point behavior still exists at the temperature near the critical one. The fixed point behavior is also appeared in the temperature dependence of normalized factorial cumulants at least from the fourth-order one. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants (or fourth-order factorial cumulants) along different freeze-out curves.

arXiv comment10 pages, 5 figures

References in corpus (43)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Signatures of the Tricritical Point in QCD
• Non-Gaussian fluctuations near the QCD critical point
• Comparison of Chemical Freeze-Out Criteria in Heavy-Ion Collisions
• Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC
• On the sign of kurtosis near the QCD critical point
• Universality, the QCD critical/tricritical point and the quark number susceptibility
• Ising Universality in Three Dimensions: A Monte Carlo Study
• QCD at finite chemical potential with six time slices
• Fluctuations as probe of the QCD phase transition and freeze-out in heavy ion collisions at LHC and RHIC
• Canonical partition function and finite density phase transition in lattice QCD
• Third moments of conserved charges as probes of QCD phase structure
• Constraining the QCD phase diagram by tricritical lines at imaginary chemical potential
• Critical Points in the Linear Sigma Model with Quarks
• Hydrodynamical evolution near the QCD critical end point
• Real time evolution of non-Gaussian cumulants in the QCD critical regime
• Meson fluctuations and thermodynamics of the Polyakov loop extended quark-meson model
• Simulation studies of fluid critical behaviour
• Centrality Dependence of Thermal Parameters Deduced from Hadron Multiplicities in Au + Au Collisions at sqrt{s_{NN}} = 130 GeV
• Acceptance dependence of fluctuation measures near the QCD critical point
• Cumulants and Correlation Functions vs the QCD phase diagram
• More efficient formulas for efficiency correction of cumulants and effect of using averaged efficiency
• Fluctuations and Correlations of Conserved Charges in QCD at Finite Temperature with Effective Models
• The kurtosis of net baryon number fluctuations from a realistic Polyakov--Nambu--Jona-Lasinio model along the experimental freeze-out line
• Nonequilibrium time evolution of higher order cumulants of conserved charges and event-by-event analysis
• Properties and uses of factorial cumulants in relativistic heavy-ion collisions
• Quartic cumulant of baryon number in the presence of QCD critical point
• Numerical equation of state and other scaling functions from an improved three-dimensional Ising model
• Correlated stopping, proton clusters and higher order proton cumulants
• Large proton cumulants from the superposition of ordinary multiplicity distributions
• Proton Cumulants and Correlation Functions in Au + Au Collisions at $\sqrt{s_{\mathrm{NN}}}$=7.7-200 GeV from UrQMD Model
• Locating the QCD critical endpoint through finite-size scaling
• Mapping the QCD phase diagram with statistics friendly distributions
• Rapidity window dependences of higher order cumulants and diffusion master equation
• Monte Carlo critical isotherms for Ising lattices
• Identifying the presence of the critical end point in QCD phase diagram by higher order susceptibilities
• Centrality dependence of chemical freeze-out parameters and strangeness equilibration in RHIC and LHC energies
• Charting the scaling region of the Ising universality class in two and three dimensions
• The sixth order cumulant of net-proton number in Binomial distribution at $\sqrt{s_{NN}}=$ 200 GeV
• Critical properties of various sizes of cluster in the Ising percolation transition
• Locating fixed points in the phase plane
• Cumulants and factorial cumulants in the 3-dimensional Ising universality class
• Generalized susceptibilities along the phase boundary of the three-dimensional, three-state Potts model