Low-temperature expansions are presented for the surface tension and second moment of the density gradient in the three-dimensional axial next-nearest-neighbor Ising model. Padé approximants for the second moment of the density gradient show a definite line of singularities in the space of coupling parameters. The surface tension is shown to be positive along this line. We conclude that our low-temperature expansion is internally consistent to seventh order, that the singularity structure we found is an exact property of the system, and that it is the roughening transition.

• Received 7 August 1992

DOI:https://doi.org/10.1103/PhysRevE.47.2317