Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-04-30
Phys.Rev.D78:045008,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
12 pages, 8 figures; one reference added; accepted for publication in PRD
Scientific paper
10.1103/PhysRevD.78.045008
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 $\lambda$).
Ebert Dietmar
Klimenko K. G.
Tyukov A. V.
Zhukovsky Ch. V.
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