Geodesics in information geometry: classical and quantum phase transitions.

We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.