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

Abstract

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 $0\le \lambda <{\lambda }_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).

Comments: 12 pages, 8 figures; one reference added; accepted for publication in PRD