Information Geometry, One, Two, Three (and Four)
D.A. Johnston🇬🇧 · W. Janke🇩🇪 · R. Kenna🇬🇧
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters, specific heats or suscept ibilities. The relative entropy induces a metric, the so-called information or Fisher-Rao m etric, on the space of parameters and the geometrical invariants of this metric carry information about the phase structure of the model. In various models the scalar curvature, , of the information metric has been found to diverge at the phase transition point and a plausible scaling relation postulated. For spin models the necessity of calculating in non-zero field has limited analytic consideration to one-dimensional, mean-field and Bethe lattice Ising models. We report on previous papers in which we extended the list somewhat in the current note by considering the {\it one}-dime nsional Potts model, the {\it two}-dimensional Ising model coupled to two-dimensional quantum gravity and the {\it three}-dimensional spherical model. We note that similar ideas have been ap plied to elucidate possible critical behaviour in families of black hole solutions in {\it four} space-time dimensions.