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First, an essential step in Wu’s analysis is the derivation of relevant lattice-dependent constants A, B, C for subnet networks. The derivation, while elementary, is tedious. Here we use a computer algorithm to evaluate them. Details of the algorithm are described in Sec. III. 

Secondly, we determine the critical frontier numerically and examine the accuracy of the homogeneity assumption. Specifically, we carry out a finite-size scaling analysis based on transfer matrix calculations to numerically determine the critical frontier for several lattice models, including the Potts model on the 3-12 and kagome-type ( $^{n}$× n ) : ( $^{n}$× n ) subnet lattices, for which the exact thresholds are not known. To assess the accuracy of the numerical determination, we also apply the procedure to models for which the exact critical thresholds are known. These include the Ising model and site percolation on the 3-12 lattice and kagome-type (1 × 1) : ( $^{n}$× n ) subnet lattices, n ≤ 6. Comparison of numerical and known exact results shows that our numerical procedure is accurate to 7 or 8 decimal places. This in turn infers that the critical frontier determined using the homogeneity assumption [9] of I is accurate to 5 decimal places or higher. 

