A model to study finite-size and magnetic effects on the phase transition of a fermion interacting system

Abstract

We present a model to study effects from an external magnetic field, chemical potential, and finite size, on the phase structure of a massive four-and six-fermion interacting system. These effects are introduced by a method of compactification of coordinates, a generalization of the standard Matsubara prescription. Through the compactification of the z coordinate and of imaginary time, we describe a heated system with the shape of a film of thickness L, at temperature β −1 undergoing first-or second-order phase transition. We have found a strong dependence of the temperature transition on the constants couplings λ and η. Besides magnetic catalysis and symmetry breaking for both kinds of transition, we have found an inverse symmetry breaking phenomenon with respect to first-order phase transition.

Charged scalar field propagator under an external magnetic field: a connection between eigenfunction and proper time methods

“…In the finite size context, we have found that the magnetic field produces the direct and inverse catalysis effects in the Gross-Neveu model in the Refs. [24,25] and [24,26], respectively. In the Nambu-Jona-Lasinio model, the IMC phenomenon at finite size was found in [27] and the MC considering finite size of the system was found in [4,28].…”