标题： 二维伊辛模型和Potts模型中次主导磁scaling场的有限尺寸校正 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校正项起着重要作用。对于二维的 Fortuin-Kasteleyn 表象下的 $Q$-态 Potts 模型，尽管次主导磁性标度场具有精确已知的指数，并且理论上预计会在有限尺寸标度分析中出现，但数值观测仍然难以捉摸，这可能是因为各种校正项的混合所致。我们模拟了六角格点上的 O($n$) 环模型，该模型与 $Q=n^2$ Potts 模型属于相同的普适类，但来自其他来源的校正项受到抑制，并为有限尺寸校正中的次主导磁性场提供了有力的数值证据。有趣的是，还观察到小簇和大簇大小区域的校正项具有相反的幅度，在特殊 $n=2$ 情况下，它们在簇大小分布的二阶矩等可观测量中相互补偿。我们的发现揭示了在有限尺寸标度分析中应该考虑次主导磁性场的影响，遗憾的是，这一影响在许多先前的研究中被忽略了。 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.