  We consider the dynamics on the C*-algebras of finite graphs obtained by
lifting the gauge action to an action of the real line. Enomoto, Fujii and
Watatani proved that if the vertex matrix of the graph is irreducible, then the
dynamics on the graph algebra admits a single KMS state. We have previously
studied the dynamics on the Toeplitz algebra, and explicitly described a
finite-dimensional simplex of KMS states for inverse temperatures above a
critical value. Here we study the KMS states for graphs with reducible vertex
matrix, and for inverse temperatures at and below the critical value. We prove
a general result which describes all the KMS states at a fixed inverse
temperature, and then apply this theorem to a variety of examples. We find that
there can be many patterns of phase transition, depending on the behaviour of
paths in the underlying graph.
