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Information Geometry, One, Two, Three (and Four) | | D.A. Johnston
; W. Janke
; R. Kenna
; | | Date: |
15 Aug 2003 | | Journal: | Acta Phys.Polon. B34 (2003) 4923-4937 | | Subject: | Statistical Mechanics | cond-mat.stat-mech hep-lat | | Abstract: | 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, ${cal R}$, 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. | | Source: | arXiv, cond-mat/0308316 | | Services: | Forum | Review | PDF | Favorites | |
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