Potts-model critical manifolds revisited
We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 6 unit cells, and the root in the temperature variable v = e K -1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagome-lattice threshold to eleven digits and that of the (3; 12 2 ) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadano phase for the lattices studied.