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

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics

Background:

• Finite-size scaling analyses are crucial for understanding critical phenomena.
• Correction terms in these analyses can arise from various sources.
• The subleading magnetic scaling field in the Q-state Potts model is theoretically expected but numerically elusive.

Purpose of the Study:

• To provide numerical evidence for the subleading magnetic field's role in finite-size corrections.
• To investigate the O(n) loop model as a system with suppressed corrections.
• To analyze the behavior of corrections in different cluster-size regions.

Main Methods:

• Simulation of the O(n) loop model on a hexagonal lattice.
• Comparison with the Q-state Potts model universality class.
• Analysis of cluster-size distribution and its moments.

Main Results:

• Strong numerical evidence for the attribution of the subleading magnetic field in finite-size corrections.
• Observation of opposite magnitudes for corrections in small and large cluster-size regions.
• Compensation of corrections in specific observables for the n=2 case.

Conclusions:

• The subleading magnetic field's effect must be considered in finite-size scaling analyses.
• Previous studies may have overlooked this crucial correction term.
• The O(n) loop model serves as a valuable tool for studying critical phenomena with reduced complexities.