Xu Yihao, Salas Jesús, Deng Youjin
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Edificio Sabatini, Leganés, 28911 Madrid, Spain.
Entropy (Basel). 2025 Apr 11;27(4):418. doi: 10.3390/e27040418.
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 -state Potts model in two dimensions, although the subleading magnetic scaling field, with exactly known exponent, is theoretically expected to give rise to finite-size-scaling analyses, numerical observation remains elusive, probably due to the mixing of various corrections. We simulate the O() loop model on the hexagonal lattice, which is in the same universality class as the Q=n2 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.
在临界现象的有限尺寸标度分析中，正确考虑可能来自不同来源的修正项起着重要作用。对于二维q态Potts模型的Fortuin-Kasteleyn表示，尽管具有精确已知指数的次主导磁标度场在理论上预期会引发有限尺寸标度分析，但数值观测仍然难以捉摸，这可能是由于各种修正的混合所致。我们在六边形晶格上模拟O(q)环模型，它与Q = n² Potts模型属于同一普适类，但抑制了来自其他来源的修正，并为有限尺寸修正中次主导磁场的归属提供了有力的数值证据。有趣的是，还观察到小簇尺寸区域和大簇尺寸区域的修正具有相反的量级，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补偿。我们的发现表明，在有限尺寸标度分析中应考虑次主导磁场的影响，而不幸的是，这在许多先前的研究中被忽略了。
