Finite-volume cumulant expansion in QCD-colorless plasma

M. Ladrem; M. A. A. Ahmed; Z. Z. Alfull; S. Cherif

doi:10.1140/epjc/s10052-015-3658-4

EPJ

Finite-volume cumulant expansion in QCD-colorless plasma

M. Ladrem¹^,2^,3^*, M. A. A. Ahmed¹^,3^,5, Z. Z. Alfull¹ and S. Cherif³^,4

¹ Physics Department, Faculty of Science, Taibah University, Al-Madinah, Al-Munawwarah, Kingdom of Saudia Arabia
² Physics Department, ENS-Vieux Kouba (Bachir El-Ibrahimi), Algiers, Algeria
³ Laboratoire de Physique et de Mathématiques Appliquées (LPMA), ENS-Vieux Kouba (Bachir El-Ibrahimi), Algiers, Algeria
⁴ Sciences and Technologies Department, Ghardaia University, Ghardaïa, Algeria
⁵ Physics Department, Taiz University in Turba, Taiz, Yemen

Received: 31 March 2015
Accepted: 28 August 2015
Published online: 16 September 2015

Abstract

Due to the finite-size effects, the localization of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite-volume transition point $T_{0}(V)$ of the QCD deconfinement phase transition to a colorless QGP, we have developed a new approach using the finite-size cumulant expansion of the order parameter and the $L_{mn}$ -method. The first six cumulants $C_{1,2,3,4,5,6}$ with the corresponding under-normalized ratios (skewness $\Sigma$ , kurtosis $\kappa$ , pentosis $\varPi _{\pm }$ , and hexosis $\mathcal {H}_{1,2,3}$ ) and three unnormalized combinations of them, ( $\mathcal {O}={\mathcal {\sigma }^{2} \mathcal {\kappa } }{\mathbf {\Sigma }^{-1} }$ , $\mathcal {U} ={\mathcal {\sigma }^{-2} \mathbf {\Sigma }^{-1} }$ , $\mathcal {N} = \mathcal {\sigma }^{2} \mathcal {\kappa }$ ) are calculated and studied as functions of (T, V). A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite-volume transition point. The extracted transition temperature value $T_{0}(V)$ agrees with that expected $T_{0}^{N}(V)$ from the order parameter and the thermal susceptibility $\chi _{T}\left( T,V\right)$ , according to the standard procedure of localization to within about $2\,\%$ . In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.

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EPJ

Finite-volume cumulant expansion in QCD-colorless plasma

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