Information geometry of the spherical model

Motivated by the observation that geometrizing statistical mechanics offers an interesting alternative to more standard approaches, we calculate the scaling behavior of the curvature R of the information geometry metric for the spherical model. We find that R~ε^-2, where ε=βc-β is the distance from criticality. The discrepancy from the naively expected scaling R~ε^-3 is explained and compared with that for the Ising model on planar random graphs, which shares the same critical exponents.