INTERFACE TENSION, EQUILIBRIUM CRYSTAL SHAPE, AND IMAGINARY ZEROS OF PARTITION-FUNCTION - PLANAR ISING SYSTEMS

For any Ising model on a planar lattice without bond crossings, we prove that the anisotropic interface tension is given by the lattice Greens function of a free random-walk problem defined on the dual lattice. This fact, derived via Vdovichenkos combinatorial method, reveals a general relation between the bulk free energy and the interface tension for two-dimensional Ising models. As an important consequence, we show that the equilibrium crystal shape corresponds to imaginary zeros of the partition function. We also discuss generalizations to non-Ising and non-solvable systems. © 1990 The American Physical Society.