  Motivated by previous observations that geometrizing statistical mechanics
offers an interesting alternative to more standard approaches,we have recently
calculated the curvature (the fundamental object in this approach) of the
information geometry metric for the Ising model on an ensemble of planar random
graphs. The standard critical exponents for this model are alpha=-1, beta=1/2,
gamma=2 and we found that the scalar curvature, R, behaves as
epsilon^(-2),where epsilon = beta_c - beta is the distance from criticality.
This contrasts with the naively expected R ~ epsilon^(-3) and the apparent
discrepancy was traced back to the effect of a negative alpha on the scaling of
R.
  Oddly,the set of standard critical exponents is shared with the 3D spherical
model. In this paper we calculate the scaling behaviour of R for the 3D
spherical model, again finding that R ~ epsilon^(-2), coinciding with the
scaling behaviour of the Ising model on planar random graphs. We also discuss
briefly the scaling of R in higher dimensions, where mean-field behaviour sets
in.
