Critical Frontier of Anisotropic Planar Potts Ferromagnets : A New Conjucture

摘要

The critical frontier of the nearest-neighbour q-state Potts ferromagnet in the fully anisotropic 3-12 lattice is conjectured through a star-triangle transformation. It recovers all the available exact results concerning particular cases, namely: (i) anisotropic square lattice for all q; (ii) anisotropic triangular and honeycomb lattices for all q; (iii) anisotropic Kagome and diced lattices for q=2; (iv) isotropic 3-12 and Asanoha lattices for q=2. It provides proposals for several other planar lattices, in particular for the anisotropic Kagome (and diced) one for q different 2, where it slightly differs from the Wu 1979 conjecture (which also satisfies the cases (i) and (iii)). The bond percolation critical probabilities on the 3-12 and Kagome lattices are determined to be respectively p sub(c) = 0.739830... and p sub(c) = 0.522372.... (Atomindex citation 14:803523)