Quark Fluctuations in a Chiral Model in the Presence of a Magnetic Field

Understanding the nature of the chiral and deconfinement phase transitions, the location of the critical point, and the properties in its vicinity are among the most important problems in the field of QCD. The purpose of this thesis is to use the two-flavor Nambu-Jona-Lasinio model in the presence of a magnetic field at the chiral limit to study the phase boundary where the spontaneously broken chiral symmetry is restored. At small chemical potential, the phase boundary exhibits a second-order phase transition. On the other hand, at large chemical potential and appropriate coupling constant, the phase boundary exhibits a first-order phase transition. Therefore, a tricritical point is expected along the phase boundary where the order of the phase transition changes. The addition of a strong magnetic field in the model is significant because strong magnetic fields are produced in off-central heavy-ion collisions, which can create the conditions for observable QCD effects. Since strong magnetic fields are also present at the core of neutron stars, this model may illuminate more about QCD in astrophysical systems