  We examine a chain of periodic arrays of 4 quantum spins with magnitudes of
1/2, 1, 3/2 and 1. There are four kinds of nearest-neighbour exchange
parameters among them. We choose two independent parameters for concreteness:
one represents the ratio of typical exchange parameters, and the other
represents a distortion. We determine the phase diagram of the ground state in
the parameter space. The phase boundaries appear as gapless lines which
separate gapful disordered phases. They are determined by the gapless equation
which was previously derived by mapping a general periodic spin chain to the
nonlinear $\sigma$ model.

Strongly Correlated Electrons;Statistical Mechanics