We report Monte Carlo simulations of a three-layer coupled q=3 Potts model on the hexagonal lattice (z=6) using Metropolis single-spin-flip dynamics. The model features intra-layer coupling β, inter-layer coupling α, and a quenched memory field w that explicitly breaks Z₃ symmetry. Through finite-size scaling analysis of system sizes L = 9, 18, 27, 36, 54, 81, 96, and 128, we extract a set of critical exponents centered on the three-body order parameter C₃. The anomalous dimension η ≈ 1. 41 and effective correlation dimension Dₑff = 2 − η ≈ 0. 59 fall outside all known two-dimensional universality classes, suggesting a new universality class driven by the irreducible three-body coupling. Five independent scaling laws (Fisher, Josephson, Rushbrooke, Widom, hyperscaling) are satisfied to residuals < 10⁻³. L = 96 and L = 128 data are preliminary; high-statistics runs are ongoing.
坤晉 江 (Tue,) studied this question.