Equilibrium crystal shapes and correlation lengths: A general exact result in two dimensions

We show that the exact equilibrium crystal shape (ECS) for a wide class of two-dimensional Ising models can simply be read off from the analytical expression for the bulk free energy: The ECS is given as the locus of purely imaginary zeros of the ``momentum''-space lattice-path propagator. From these shapes, one may obtain numerically, to arbitrary accuracy, the high-temperature direction-dependent correlation lengths of the dual system. These exact ECS's and corresponding correlation lengths were previously known only for the rectangular, triangular, and honeycomb lattices.