  We define geometric critical exponents for systems that undergo continuous
second order classical and quantum phase transitions. These relate scalar
quantities on the information theoretic parameter manifolds of such systems,
near criticality. We calculate these exponents by approximating the metric and
thereby solving geodesic equations analytically, near curvature singularities
of two dimensional parameter manifolds. The critical exponents are seen to be
the same for both classical and quantum systems that we consider, and we
provide evidence about the possible universality of our results.
