Exact finite-size scaling functions of the interfacial tensions are obtained for the Ising model with isotropic coupling on a set of $M\times N$ planar lattices, including square (sq), plane triangular (pt), and honeycomb (hc) lattices. The analyses of transitive behaviors at criticality revise the knowledge of the interfacial tensions as a function of the aspect ratio defined by $R=M∕N$ for $R$ approaching to zero gradually. The amplitudes of the interfacial tensions for the sq, pt, and hc lattices are further shown to have relative proportions $1:\sqrt{3}∕2:\sqrt{3}$ which are related to the aspect ratios for the three lattices to have similar domains.

• Received 15 November 2005

DOI:https://doi.org/10.1103/PhysRevE.73.046135