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, 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
