标题： 二维伊辛模型和庞特模型中来自次主导磁性标度场的有限尺寸修正 显示英文标题

标题： Finite-size corrections from the subleading magnetic scaling field for the Ising and Potts models in two dimensions

摘要： 在临界现象的有限尺寸标度分析中，正确考虑来自不同来源的修正项起着重要作用。 对于二维平面中$Q$状态 Potts 模型的 Fortuin-Kasteleyn 表示，尽管次级磁标度场的指数已知精确值，理论上预期它会在有限尺寸标度分析中出现，但由于各种修正的混合，数值观察仍然难以捉摸。 我们在六边形晶格上模拟了 O($n$) 环模型，该模型与$Q=n^2$Potts 模型处于同一普适类，但其他来源的修正被抑制，为有限尺寸修正中次级磁场的归属提供了强有力的数值证据。 有趣的是，还观察到小簇和大簇区域的修正具有相反的大小，并且对于特殊的$n=2$情况，它们在诸如簇尺寸分布的二阶矩等可观测量中相互抵消。 我们的发现表明，在有限尺寸标度分析中应考虑到次级磁场的影响，而这一影响在许多先前的研究中不幸被忽略了。 显示英文摘要

摘要： In finite-size scaling analyses of critical phenomena, proper consideration of correction terms, which can come from different sources, plays an important role. For the Fortuin-Kasteleyn representation of the $Q$-state Potts model in two dimensions, although the subleading magnetic scaling field, with exactly known exponent, is theoretically expected to give rise in finite-size-scaling analyses, numerical observation remains elusive probably due to the mixing of various corrections. We simulate the O($n$) loop model on the hexagonal lattice, which is in the same universality class as the $Q=n^2$ Potts model but has suppressed corrections from other sources, and provides strong numerical evidence for the attribution of the subleading magnetic field in finite-size corrections. Interestingly, it is also observed that the corrections in small- and large-cluster-size regions have opposite magnitudes, and, for the special $n=2$ case, they compensate with each other in observables like the second moment of the cluster-size distribution. Our finding reveals that the effect of the subleading magnetic field should be taken into account in finite-size-scaling analyses, which was unfortunately ignored in many previous studies.