  We study the Landau-Ginzburg models which correspond to Calabi-Yau
four-folds. We construct the index of the typical states which correspond to
toric divisors. This index shows that whether a corresponding divisor can
generate a non-perturbative superpotential. For an application, we consider the
phase transition in terms of the orbifold construction. We obtain the simple
method by which the divisor, which can not generate a superpotential in the
original theory, can generate a superpotential after orbifoldization.
