  Although the notion of entropy lies at the core of statistical mechanics, it
is not often used in statistical mechanical models to characterize phase
transitions, a role more usually played by quantities such as various order
parameters, specific heats or suscept ibilities. The relative entropy induces a
metric, the so-called information or Fisher-Rao m etric, on the space of
parameters and the geometrical invariants of this metric carry information
about the phase structure of the model.
  In various models the scalar curvature, ${\cal R}$, of the information metric
has been found to diverge at the phase transition point and a plausible scaling
relation postulated. For spin models the necessity of calculating in non-zero
field has limited analytic consideration to one-dimensional, mean-field and
Bethe lattice Ising models. We report on previous papers in which we extended
the list somewhat in the current note by considering the {\it one}-dime nsional
Potts model, the {\it two}-dimensional Ising model coupled to two-dimensional
quantum gravity and the {\it three}-dimensional spherical model. We note that
similar ideas have been ap plied to elucidate possible critical behaviour in
families of black hole solutions in
  {\it four} space-time dimensions.
