标题： 四点归一化耦合常数在O(N)模型中 显示英文标题

标题： Four-point renormalized coupling constant in O(N) models

摘要： 重整化零动量四点耦合$g_r$的$O(N)$不变标量场理论在$d$维度中通过应用$1/N$展开和强耦合分析进行研究。 $O(1/N)$修正对$\beta$函数和固定点值$g_r^*$进行了显式计算。 近临界区域对格点非线性$\sigma$模型的强耦合级数进行了分析，在$d=2$和$d=3$中针对多个$N$值以及对应的$g_r^*$值进行了提取。 大$N$和强耦合结果相互比较，发现具有良好的总体一致性。 对于较小的$N$，二维中的强耦合分析目前对$g^*_r$的确定最为准确（或对于$N=2,3$与现有的蒙特卡罗估计相当），在三维中它与现有的$\phi^4$场论结果一致。 显示英文摘要

摘要： The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function and to the fixed point value $g_r^*$ are explictly computed. Strong coupling series for lattice non-linear $\sigma$ models are analyzed near criticality in $d=2$ and $d=3$ for several values of $N$ and the corresponding values of $g_r^*$ are extracted. Large-$N$ and strong coupling results are compared with each other, finding a good general agreement. For small $N$ the strong coupling analysis in 2-d gives the best determination of $g^*_r$ to date (or comparable for $N=2,3$ with the available Monte Carlo estimates), and in 3-d it is consistent with available $\phi^4$ field theory results.