Thermodynamics of magnetized BPS baryonic layers and the effects of the isospin chemical potential

Through the Hamilton-Jacobi equation of classical mechanics, BPS magnetized Baryonic layers (possessing both baryonic charge and magnetic flux) have been constructed in the gauged non-linear sigma model (G-NLSM) minimally coupled to Maxwell theory, which is one of the most relevant effective theories for Quantum Chromodynamics (QCD) in the strongly interacting low-energy limit which also takes into account the electromagnetic interactions. Since the topological charge that naturally appears on the right hand side of the BPS bound is a non-linear function of the baryonic charge, the thermodynamics of these magnetized Baryonic layers is highly non-trivial. In this work, using tools from the theory of Casimir effect, we derive analytical relationship between baryonic charge, topological charge, magnetic flux and relevant thermodynamical quantities (such as pressure, specific heat and magnetic susceptibility) of these layers. The critical Baryonic chemical potential is identified. Quite interestingly, the grand canonical partition function can be related with the Riemann zeta function. On the technical side, it is quite a remarkable result to derive explicit expressions for all these thermodynamics quantities of a strongly interacting magnetized system at finite Baryon density. The effects of the Isospin chemical potential can be included as well: in particular, we will be able to construct explicitly the BPS bound and the corresponding BPS configurations also in the case in which the Isospin chemical potential is non-zero. The physical interpretations of our analytical results will be discussed.