标题： 对于$SO(4)$主子色模型的连续极限测试以及对$Ł_\MS$的预测 显示英文标题

标题： Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and the prediction for $Ł_\MS$

摘要： 我们研究了连续极限下的$SO(N)$主场模型，在细节上重点关注了$SO(4)$模型及其覆盖群 SU(2)xSU(2)。 我们用 Lambda_MS 表达质量间隙，并与 Hollowood 对$m/\L_\MS = 3.8716$的预测进行比较。 我们使用 Lüscher 等人的有限尺寸缩放方法来推导$m/\L_\MS$，并发现对于$SO(4)$模型，计算得到的$m/\L_\MS \sim 14$结果与理论存在强烈分歧；但对 SU(2)xSU(2) 进行类似的分析则与理论结果非常吻合。 我们推测，对于 $SO(4)$ 违背有限尺度标度假设的情况，在所研究的相关长度 $\xi$ 的值下非常严重，并且尽管我们的尝试将结果外推到零晶格间距看起来合理，但结果是错误的。 相反，在 SU(2)xSU(2) 模拟中，有限尺度标度的违背与微扰理论一致，并且计算得到的 $beta-$函数与在尺度 $L/a \le \xi$ 上评估的耦合的 3-圈近似值吻合得很好，其中 $\xi$ 以晶格间距 $a$ 为单位测量。 我们推测，晶格涡旋效应在 $SO(4)$ 模型中导致连续极限的出现被推迟，直到获得更大的相关长度，尽管表面上已经出现了标度行为。 给出了 SO(N) m 的质量谱结果，N=8,10，将其与理论进行比较，为我们提出的想法提供了合理的支持。 显示英文摘要

摘要： We investigate the continuum limit in $SO(N)$ Principal Chiral Models concentrating in detail on the $SO(4)$ model and its covering group SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the prediction of Hollowood of $m/\L_\MS = 3.8716$. We use the finite-size scaling method of L\"uscher et al. to deduce $m/\L_\MS$ and find that for the $SO(4)$ model the computed result of $m/\L_\MS \sim 14$ is in strong disagreement with theory but that a similar analysis of the SU(2)xSU(2) yields excellent agreement with theory. We conjecture that for $SO(4)$ violations of the finite-size scaling assumption are severe forthe values of the correlation length, $\xi$, investigated and that our attempts to extrapolate the results to zero lattice spacing, although plausible, are erroneous. Conversely, the finite-size scaling violations in the SU(2)xSU(2) simulation are consistent with perturbation theory and the computed $beta-$function agrees well with the 3-loop approximation for couplings evaluated at scales $L/a \le \xi$, where $\xi$ is measured in units of the lattice spacing, $a$. We conjecture that lattice vortex artifacts in the $SO(4)$ model are responsible for delaying the onset of the continuum limit until much larger correlation lengths are achieved notwithstanding the apparent onset of scaling. Results for the mass spectrum for SO(N) m, N=8,10 are given whose comparison with theory gives plausible support to our ideas.