  An expansion in inverse spin anisotropy, which enables us to study the
behaviour of discrete spin models as the spins soften, is developed. In
particular we focus on models, such as the chiral clock model and the $p$-state
clock model with competing first and second neighbour interactions, where there
are special multiphase points at zero temperature at which an infinite number
of ground states are degenerate. The expansion allows calculation of the ground
state phase diagram near these points as the spin anisotropy, which constrains
the spin to take discrete values, is reduced from infinity. Several different
behaviours are found, from a single first order phase boundary to infinite
series of commensurate phases.
