Critical properties of various sizes of cluster in the Ising percolation transition

Abstract

It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed.

arXiv comment12 pages, 5 figures. Accepted by IJMPE

References in corpus (22)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Non-Gaussian fluctuations near the QCD critical point
• The QCD transition temperature: results with physical masses in the continuum limit II.
• Chiral crossover in QCD at zero and non-zero chemical potentials
• Energy Dependence of Moments of Net-proton Multiplicity Distributions at RHIC
• On the sign of kurtosis near the QCD critical point
• Slowing Out of Equilibrium Near the QCD Critical Point
• Beam energy dependence of moments of the net-charge multiplicity distributions in Au+Au collisions at RHIC
• Scale for the Phase Diagram of Quantum Chromodynamics
• Canonical partition function and finite density phase transition in lattice QCD
• Non-monotonic energy dependence of net-proton number fluctuations
• Critical Points in the Linear Sigma Model with Quarks
• Collision Energy Dependence of Moments of Net-Kaon Multiplicity Distributions at RHIC
• Masses and decay constants of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ from $N_f=2$ lattice QCD close to the physical point
• Observation of the critical end point in the phase diagram for hot and dense nuclear matter
• De-Confinement and Clustering of Color Sources in Nuclear Collisions
• Examining the crossover from hadronic to partonic phase in QCD
• De-Confinement in high multiplicity proton-proton collisions at LHC energies
• Baseline for the cumulants of net-proton distributions at STAR
• Percolation Approach to Initial Stage Effects in High Energy Collisions
• Locating fixed points in the phase plane

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