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A metric is introduced on the two dimensional space of parameters describingthe Ising model on a Bethe lattice of co-ordination number q. The geometryassociated with this metric is analysed and it is shown that the Gaussiancurvature diverges at the critical point. For the special case q=2 thecurvature reduces to an already known result for the one dimensional Isingmodel. The Gaussian curvature is also calculated for a general ferro-magnetnear its critical point, generalising a previous result for t>0. The generalexpression near a critical point is compared with the specific case of theBethe lattice and a subtlety, associated with the fact that the specific heatexponent for the Bethe lattice vanishes, is resolved.

Geometry and thermodynamic fluctuations of the Ising model on a Bethe lattice