  It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature $\beta$ and external field $h$.
  In various two parameter calculable models the scalar curvature ${\cal R}$ of
the information metric has been found to diverge at the phase transition point
$\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta-
\beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2,
\gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find
${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced
back to the effect of a negative $\alpha$.
