论文标题
$θ$依赖性在小$ n $限制$ 2D $ $ CP^{n-1} $型号
$θ$-dependence in the small-$N$ limit of $2d$ $CP^{N-1}$ models
论文作者
论文摘要
我们提出了一项$θ$依赖性的系统数值研究，左右在$θ= 0 $的小$ n $限制中，$ 2D $ $ CP^{n-1} $型号，旨在阐明在连续限制中可能存在不同的拓扑敏感性。我们遵循两倍的策略，基于直接模拟的一方面，以$ n = 2 $和$ n = 3 $的相关长度，相关长度高达$ o（10^2）$，而另一侧则以$ n $ $ n $最高$ 9 $获得的$ n $ n $外推结果的外推。基于此，我们为$ n = 3 $的有限拓扑敏感性提供了结论性证据，并具有连续估计$ξ^2χ= 0.110（5）$。另一方面，以$ n = 2 $获得的结果仍然尚无定论：它们与对数发散的连续性外推的一致，但尚未排除有限的连续值，$ n $ n $ n $ lighte the $ n $在这种情况下是$ n $。最后，对于$θ$依赖性的非二次部分获得的结果，尤其是对于所谓的$ b_2 $系数，与$θ$依赖性在$θ$依赖性匹配的结果一致，该稀释式instanton气体近似在$ξ^2χ$ diverges的点处。
We present a systematic numerical study of $θ$-dependence around $θ=0$ in the small-$N$ limit of $2d$ $CP^{N-1}$ models, aimed at clarifying the possible presence of a divergent topological susceptibility in the continuum limit. We follow a twofold strategy, based on one side on direct simulations for $N = 2$ and $N = 3$ on lattices with correlation lengths up to $O(10^2)$, and on the other side on the small-$N$ extrapolation of results obtained for $N$ up to $9$. Based on that, we provide conclusive evidence for a finite topological susceptibility at $N = 3$, with a continuum estimate $ξ^2 χ= 0.110(5)$. On the other hand, results obtained for $N = 2$ are still inconclusive: they are consistent with a logarithmically divergent continuum extrapolation, but do not yet exclude a finite continuum value, $ξ^2 χ\sim 0.4$, with the divergence taking place for $N$ slightly below 2 in this case. Finally, results obtained for the non-quadratic part of $θ$-dependence, in particular for the so-called $b_2$ coefficient, are consistent with a $θ$-dependence matching that of the Dilute Instanton Gas Approximation at the point where $ξ^2 χ$ diverges.
