  In this paper we investigate the phase structure of a (1+1) and
(3+1)-dimensional quark model with four-quark interaction and in the presence
of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical
potentials. It is shown that the chemical potential $\mu_{I5}$ promotes the
appearance of the charged PC phase with nonzero baryon density. Results of both
models are qualitatively the same, this fact enhances one's confidence in %the
faith in the obtained predictions. It is established that in the large-$N_c$
limit ($N_c$ is the number of colored quarks) there exists a duality
correspondence between the chiral symmetry breaking phase and the charged pion
condensation one.
