  A metric is introduced on the space of parameters (couplings) describing the
large N limit of the O(N) model in Euclidean space. The geometry associated
with this metric is analysed in the particular case of the infinite volume
limit in 3 dimensions and it is shown that the Ricci curvature diverges at the
ultra-violet (Gaussian) fixed point but is finite and tends to constant
negative curvature at the infra-red (Wilson-Fisher) fixed point. The
renormalisation group flow is examined in terms of geodesics of the metric. The
critical line of cross-over from the Wilson-Fisher fixed point to the Gaussian
fixed point is shown to be a geodesic but all other renormalisation group
trajectories, which are repulsed from the Gaussian fixed point in the
ultra-violet, are not geodesics. The geodesic flow is interpreted in terms of a
maximisation principle for the relative entropy.
