arXiv 0804.48262008-04hep-phhep-th

具有同位旋化学势的Gross-Neveu模型中的有限尺寸效应

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

D. Ebert, K. G. Klimenko, A. V. Tyukov, V. Ch. Zhukovsky

备注：: 12 pages, 8 figures; one reference added; accepted for publication in PRD
发表信息：: Phys.Rev.D78:045008,2008
DOI：: 10.1103/PhysRevD.78.045008

摘要：

研究了具有紧化空间坐标的（1+1）维$R^1\times S^1$时空中存在同位旋化学势$μ_I$时两味Gross-Neveu模型的性质.在极限$N_c\to\infty$中进行考虑，即在具有无限数量的色夸克的情况下。结果表明，在$L=\infty$（$L$是圆周$S^1$的长度）处，对任意小的非零$μ_I$都能实现π凝聚相.在有限的$L$值下，对于夸克场的周期边界条件和反周期边界条件，得到了模型关于参数$ν\simμ_I$和$λ\sim 1/L$的相图.结果表明，在$(λ,ν)$平面上，存在一个整体位于π凝聚相内部的带$0\leλ<λ_c$。在这一阶段，π凝聚间隙是一个振荡函数与$λ$（在固定$ν$）和$ν$（在固定$λ$）。

英文摘要：

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 $μ_I$. 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 $μ_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $ν\simμ_I$ and $λ\sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(λ,ν)$ there is a strip $0\leλ<λ_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $λ$ (at fixed $ν$) and $ν$ (at fixed $λ$).

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