Phase transition in a four-dimensional fermion model

We study the four-dimensional self-coupled massless fermion model with a dynamical breakdown of chiral symmetry through an emergence of collective excitations and discuss a phase transition under the influence of both temperature T and fermion-number density n. We give the self-consistency equation which determines an amount of dynamically generated fermion mass as a function of T and n. Using the numerical solutions of the self-consistency equation, we derive the effective potential of the collective excitations. We show that the model has a second-order phase transition at a critical temperature and also a critical density and that the dynamical symmetry violation vanishes above these critical values. We also draw the phase diagram in the T-n plane for several values of the generated fermion mass.