  The generally accepted phase diagrams for the discrete $Z_N$ spin models in
two dimensions imply the existence of certain renormalisation group flows, both
between conformal field theories and into a massive phase. Integral equations
are proposed to describe these flows, and some properties of their solutions
are discussed. The infrared behaviour in massless and massive directions is
analysed in detail, and the techniques used are applied to a number of other
models.
