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We investigate the hadron-quark phase transition at finite density in thepresence of a magnetic field taking into account the anisotropy created by auniform magnetic field in the system's equations of state. We find a newanisotropic equilibrium condition that will drive the first-order phasetransition along the boundary between the two phases. Fixing the magnetic fieldin the hadronic phase, the phase transition is realized by increasing thebaryonic chemical potential at zero temperature. It is shown that the magneticfield is mildly boosted after the system transitions from the hadronic to thequark phase. The magnetic-field discontinuity between the two phases issupported by a surface density of magnetic monopoles, which accumulate at theboundary separating the two phases. The mechanism responsible for the monopolecharge density generation is discussed. Each phase is found to be paramagneticwith higher magnetic susceptibility in the quark phase. The connection with thephysics of neutron stars is highlighted through out the paper.

Hadron-Quark Phase Transition at Finite Density in the Presence of a Magnetic Field: Anisotropic Approach