Regularization influence and topological effects on the phase transition of a scalar theory

In this paper, we examine a spin-zero gas subject to self-interaction of the type [Formula: see text] under spatial confinement with different boundary conditions. By using the well-known expansion in Feynman graphs, we calculate the effective potential of the model in one-loop order. Furthermore, we employ quantum field theory in a toroidal topology to analyze the system’s phase structure. Additionally, we apply several regularization prescriptions in calculating the corrected mass parameter of the system, all of them independent of the thermo-topological terms. This parameter was used to obtain the free energy density of the model, revealing that it undergoes a second-order phase transition. Once the finite volume occupied by the system has been specified and the regularization chosen technique, we found that periodic boundary conditions induce lower critical temperatures on the theoretical model considered here in relation to antiperiodic boundary conditions. Quasiperiodic boundary conditions presented intermediate behavior.