Finite size effects in the Gross-Neveu model with isospin chemical potential

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional \(R^1\times S^1\) spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential \(\mu_I\). The consideration is performed in the limit \(N_c\to\infty\), i.e. in the case with infinite number of colored quarks. It is shown that at \(L=\infty\) (\(L\) is the length of the circumference \(S^1\)) the pion condensation phase is realized for arbitrary small nonzero \(\mu_I\). At finite values of \(L\), the phase portraits of the model in terms of parameters \(\nu\sim\mu_I\) and \(\lambda\sim 1/L\) are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane \((\lambda,\nu)\) there is a strip \(0\le\lambda