Finite Size Scaling of the Ising Interfacial Tension

Michael J. E. O’Rourke

Atsushi Yamagata

Goranka Bilalbegović

Martin Hasenbusch B, K. Pinn

Ming‐Chya Wu

Exact finite-size scaling functions of the interfacial tensions are obtained for the Ising model with isotropic coupling on a set of M x 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:square root of 3 / 2:square root of 3 which are related to the aspect ratios for the three lattices to have similar domains.

K. K. Mon, David Jasnow

The interfacial tension of the simple-cubic Ising model near the transition temperature has been calculated with use of an extension of a recently proposed novel Monte Carlo method. Finite-size scaling theory was used to analyze the results and to obtain the surface tension amplitude. Universal ratios involving the surface tension amplitude are evaluated. Previous ambiguities in the theoretical value of the ratio involving the surface tension and specific-heat amplitudes have been clarified.