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1. Hadron-quark phase transition at finite density in the presence of a magnetic field: Anisotropic approach

   https://doi.org/10.1142/S0217751X22500488  

   Ferrer, E. J.; Hackebill, A. (March 2022, International Journal of Modern Physics A)

   We investigate the hadron-quark phase transition at finite density in the presence of a magnetic field taking into account the anisotropy created by a uniform magnetic field in the system’s equations of state. We find a new anisotropic equilibrium condition that will drive the first-order phase transition along the boundary between the two phases. Fixing the magnetic field in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic field is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic-field discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper. 

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2. Hadron-quark phase transition at finite density in the presence of a magnetic eld: Anisotropic approach

   https://doi.org/doi.org/10.3390/universe7120458  

   E. J. Ferrer and A. Hackebill (May 2022, International journal of modern physics A)

   World Scientific (Ed.)

   We investigate the hadron-quark phase transition at nite density in the presence of a magnetic eld taking into account the anisotropy created by a uniform magnetic eld in the system's equations of state.We fi nd a new anisotropic equilibrium condition that will drive the fi rst-order phase transition along the boundary between the two phases. Fixing the magnetic eld in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic eld is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic- eld discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper. 

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3. Quark Matter in Neutron Stars

   https://doi.org/10.1007/978-3-030-34234-0_9  

   Spinella, W.; Weber, F.; Contrera, G.; Orsaria, M. G. (April 2020, Discoveries at the Frontiers of Science: From Nuclear Astrophysics to Relativistic Heavy Ion Collisions)

   The nonlocal three-flavor Nambu-Jona-Lasinio model is used to study quark deconfinement in the cores of neutron stars (NSs). The quark-hadron phase transition is modeled using both the Maxwell construction and the Gibbs construction. For the Maxwell construction, we find that all NSs with core densities beyond the phase transition density are unstable. Therefore, no quark matter cores would exist inside such NSs. The situation is drastically different if the phase transition is treated as a Gibbs transition, resulting in stable NSs whose stellar cores are a mixture of hadronic matter and deconfined quarks. The largest fractions of quarks achieved in the quark-hadron mixed phase are around 50%. No choice of parametrization or composition leads to a pure quark matter core. The inclusion of repulsive vector interactions among the quarks is crucial since the equation of state (EoS) in the quark-hadron mixed phase is significantly softer than that of the pure hadronic phase. 

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4. Effect of Strong Magnetic Field on Competing Order Parameters in Two-Flavor Dense Quark Matter

   https://doi.org/10.1155/2017/6472909  

   Mandal, Tanumoy; Jaikumar, Prashanth (January 2017, Advances in High Energy Physics)

   We study the effect of strong magnetic field on competing chiral and diquark order parameters in a regime of moderately dense quark matter. The interdependence of the chiral and diquark condensates through nonperturbative quark mass and strong coupling effects is analyzed in a two-flavor Nambu-Jona-Lasinio (NJL) model. In the weak magnetic field limit, our results agree qualitatively with earlier zero-field studies in the literature that find a critical coupling ratio G D / G S ~ 1.1 below which chiral or superconducting order parameters appear almost exclusively. Above the critical ratio, there exists a significant mixed broken phase region where both gaps are nonzero. However, a strong magnetic field B ≳ 1 0 18  G disrupts this mixed broken phase region and changes a smooth crossover found in the weak-field case to a first-order transition for both gaps at almost the same critical density. Our results suggest that in the two-flavor approximation to moderately dense quark matter strong magnetic field enhances the possibility of a mixed phase at high density, with implications for the structure, energetics, and vibrational spectrum of neutron stars. 

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5. Magnetic-field Induced Deformation in Hybrid Stars

   https://doi.org/10.3847/1538-4357/aca85c  

   Rather, Ishfaq A.; Rather, Asloob A.; Lopes, Ilídio; Dexheimer, V.; Usmani, A. A.; Patra, S. K. (January 2023, The Astrophysical Journal)

   Abstract The effects of strong magnetic fields on the deconfinement phase transition expected to take place in the interior of massive neutron stars are studied in detail for the first time. For hadronic matter, the very general density-dependent relativistic mean field model is employed, while the simple, but effective vector-enhanced bag model is used to study quark matter. Magnetic-field effects are incorporated into the matter equation of state and in the general-relativity solutions, which also satisfy Maxwell’s equations. We find that for large values of magnetic dipole moment, the maximum mass, canonical mass radius, and dimensionless tidal deformability obtained for stars using spherically symmetric Tolman–Oppenheimer–Volkoff (TOV) equations and axisymmetric solutions attained through the LORENE library differ considerably. The deviations depend on the stiffness of the equation of state and on the star mass being analyzed. This points to the fact that, unlike what was assumed previously in the literature, magnetic field thresholds for the approximation of isotropic stars and the acceptable use of TOV equations depend on the matter composition and interactions. 

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