Comment on ‘Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras’

Abstract

We present an algorithm to compute the exact critical probability h(n) for an n×∞ helical square lattice with random and independent site occupancy. The algorithm has time complexity O(n2cn) and space complexity O(cn) with c = 2.7459... and allows us to compute h(n) up to n = 24. Since the extrapolation result of h(n) is inconsistent with the current best estimation of pc , we also compute and extend the exact critical probability pc(n) for an n×∞ cylindrical square lattice to n = 24. Our calculation shows that the current best result of pc=0.59274605079210(2) by Jacobsen (2015 J. Phys. A: Math. Theor. 48 454003) is incorrect and the corrected value should be 0.5927460507896(1) .