Journal of Statistical Physics, Vol. 67, Nos. 3/4, 1992, p. 449-470.
We study the thermodynamic limit of the orientation-dependent surface tension.
Under general conditions, which we show to hold true for a large class of lattice
systems, we prove that the limit exists and that it satisfies some convexity
properties related to the pyramidal inequality introduced by R.L. Dobrushin
and S.B. Shlosman. We discuss some consequences of these results for the
equilibrium crystal shape.