  The $q=2$ random cluster model is studied in the context of two mean field
models: The Bethe lattice and the complete graph. For these systems, the
critical exponents that are defined in terms of finite clusters have some
anomalous values as the critical point is approached from the high density side
which vindicates the results of earlier studies. In particular, the exponent
$\tilde \gamma^\prime$ which characterises the divergence of the average size
of finite clusters is 1/2 and $\tilde\nu^\prime$, the exponent associated with
the length scale of finite clusters is 1/4. The full collection of exponents
indicates an upper critical dimension of 6. The standard mean field exponents
of the Ising system are also present in this model ($\nu^\prime = 1/2$,
$\gamma^\prime = 1$) which implies, in particular, the presence of two
diverging length scales. Furthermore, the finite cluster exponents are stable
to the addition of disorder which, near the upper critical dimension, may have
interesting implications concerning the generality of the disordered
system/correlation length bounds.
