论文标题
$ 2D〜 \ MATHRM {CP}^1 $或$ \ MATHRM {o}（3）$ non-linear $σ$ -Model：它是否发散吗？
Topological susceptibility of $2d~\mathrm{CP}^1$ or $\mathrm{O}(3)$ non-linear $σ$-model: is it divergent or not?
论文作者
论文摘要
$ 2D $ $ \ MATHRM {cp}^{n-1} $模型的拓扑敏感性是基于扰动计算的，可以在限制$ n \至2 $的情况下开发差异，其中这些模型还原为众所周知的非线性$ \ mathrm {o}（O}（3）$ $ $ - $ -Model。差异是由于任意尺寸的激体位的主导地位，并且它通过数值晶格模拟的检测很困难，因为它在晶格间距中是对数。我们从不同的角度解决了问题，研究体积以无量纲晶格单元固定时，研究模型的行为，在这些晶格单元中，扰动预测将变成更容易可检查的行为。在以$ n = 3 $和$ 4 $的方式测试此策略之后，我们将其应用于$ n = 2 $，同时采用了一种多动算法来克服在渐近小晶格上罕见的拓扑波动的问题。我们的最终结果通过纯粹的非扰动方法充分证实了$ 2D $ $ \ MATHRM {CP}^1 $模型的拓扑敏感性的差异。
The topological susceptibility of $2d$ $\mathrm{CP}^{N-1}$ models is expected, based on perturbative computations, to develop a divergence in the limit $N \to 2$, where these models reduce to the well-known non-linear $\mathrm{O}(3)$ $σ$-model. The divergence is due to the dominance of instantons of arbitrarily small size and its detection by numerical lattice simulations is notoriously difficult, because it is logarithmic in the lattice spacing. We approach the problem from a different perspective, studying the behavior of the model when the volume is fixed in dimensionless lattice units, where perturbative predictions are turned into more easily checkable behaviors. After testing this strategy for $N = 3$ and $4$, we apply it to $N = 2$, adopting at the same time a multicanonic algorithm to overcome the problem of rare topological fluctuations on asymptotically small lattices. Our final results fully confirm, by means of purely non-perturbative methods, the divergence of the topological susceptibility of the $2d$ $\mathrm{CP}^1$ model.
