Finite-Size Corrections from the Subleading Magnetic Scaling Field for the Ising and Potts Models in Two Dimensions

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 to 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=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.