Research Article QCD Thermodynamics and Magnetization in Nonzero Magnetic Field Abdel Nasser Tawfik, 1,2 Abdel Magied Diab, 1,2 Nada Ezzelarab, 1,2 and Asmaa G. Shalaby 2,3 1 Egyptian Center for Teoretical Physics (ECTP), Modern University for Technology and Information (MTI), Cairo 11571, Egypt 2 World Laboratory for Cosmology And Particle Physics (WLCAPP), Cairo 11571, Egypt 3 Physics Department, Benha University, Benha 13815, Egypt Correspondence should be addressed to Abdel Nasser Tawfk; a.tawfk@eng.mti.edu.eg Received 7 October 2015; Accepted 26 January 2016 Academic Editor: Juan Jos´ e Sanz-Cillero Copyright © 2016 Abdel Nasser Tawfk et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te publication of this article was funded by SCOAP 3 . In nonzero magnetic feld, the magnetic properties and thermodynamics of the quantum-chromodynamic (QCD) matter are studied in the hadron resonance gas and the Polyakov linear-sigma models and compared with recent lattice calculations. Both models are fairly suited to describe the degrees of freedom in the hadronic phase. Te partonic ones are only accessible by the second model. It is found that the QCD matter has paramagnetic properties, which monotonically depend on the temperature and are not afected by the hadron-quark phase transition. Furthermore, raising the magnetic feld strength increases the thermodynamic quantities, especially in the hadronic phase, but reduces the critical temperature, that is, inverse magnetic catalysis. 1. Introduction In peripheral heavy-ion collisions, a strong and very localized magnetic feld is likely generated. Te opposite relativistic motion of the spectator’s positive charges and the imbalance in the momentum of the participants together contribute to generating such short-lived and huge magnetic feld (∼ 10 19 Gauss), which apparently should come up with signif- cant efects on the quantum-chromodynamic (QCD) matter. Tese efects can be coupled to experimental observables; for instance, in the STAR experiment at the relativistic heavy-ion collider (RHIC), ||∼ 2  [1, 2], and in ALICE experiment at the large hadron collider (LHC), || ∼ 10–15 2  [1, 2], where || is the net electric charge and   is the pion mass [3]. Only in heavy-ion collisions do the self-generating magnetic felds play an essential role. Te early universe and magnetors (special types of neutron stars), for instance, should extremely be afected by such felds, which are conjectured to infuence even the acceleration of various cosmic rays and the creation of stars [4]. Tey can mediate important processes afecting the dynamics, the distribution, and even the composition of the galactic plasmas, for instance [4]. Te infuences of magnetic felds on the hadronic matter and on the phase-space structure of quark-gluon plasma (QGP) are included in various models, such as hadron reso- nance gas (HRG) [5, 6], and estimated in lattice QCD simula- tions [7–12]. Te Polyakov-Nambu-Jona-Lasinio (PNJL) and NJL models are examples on QCD-like models in which such magnetic efects were estimated [13–16]. Coupling Polyakov loops to the linear-sigma model (PLSM) introduces color charge interactions to the pure gauge feld. PLSM reveals interesting features about the response of QCD matter to fnite magnetic feld [17, 18]. Recently, electric conductivity in thermal medium and the phase structure of the strongly interacting matter in presence of magnetic feld have been reported [19–22]. In the present work, we plan to utilize the HRG and PLSM approaches in fnite magnetic feld in order to study the QCD equation-of-state (EoS). Furthermore, it intends to estimate diferent thermodynamic observables including pressure, entropy, energy densities, and magnetization by using the modifed energy-momentum dispersion relations which arise from fnite magnetic feld. Also, we verify that the thermal QCD medium is paramagnetic, especially at Hindawi Publishing Corporation Advances in High Energy Physics Volume 2016, Article ID 1381479, 8 pages http://dx.doi.org/10.1155/2016/1381479