For pt.I see ibid., vol.10, no.12, p.2769 (1980). The general theory, developed in the preceding paper to study the ground state properties of spin glasses, is applied to two-component spin systems. As an extension of the Edwards-Anderson model (1975) a system of the two-component spins, each spin of which can take only n directions in a plane ('discrete planar model'), is introduced to count ... [Show full abstract] (gn)-the average degeneracy in the ground state. This procedure allows the authors to see how the fundamental properties change by the spin symmetry. For n=2, the theory reproduces the previous results for the Ising model. They can study the XY model as a limit of n to infinity . Precise calculations are performed for the infinite-range exchange interactions. They find (ginfinity )=e0.51691N.