Finite-size effects on the phase transition in a four- and six-fermion interaction model

•First- and second-order phase transitions occur in fermion self-interaction models.•Minimal size of the system exists for phase transitions to be sustained.•Four- and six-fermion interaction models describe inverse symmetry breaking.

We consider four- and six-fermion interacting models at finite temperature and density. We construct the corresponding free energies and investigate the appearance of first- and second-order phase transitions. Finite-size effects on the phase structure are investigated using methods of quantum field theory on toroidal topologies.