A relation between moduli space of D-branes on orbifolds and Ising model

We study D-branes transverse to an abelian orbifold C^3/Z_n Z_n. The moduli space of the gauge theory on the D-branes is analyzed by combinatorial calculation based on toric geometry. It is shown that the calculation is related to a problemto count the number of ground states of an antiferromagnetic Ising model. The lattice on which the Ising model is defined is a triangular one defined on the McKay quiver of the orbifold.