The information geometry of the onedimensional Potts model
Abstract
In various statisticalmechanical models the introduction of a metric into the space of parameters (e.g. the temperature variable, β, and the external field variable, h, in the case of spin models) gives an alternative perspective on the phase structure. For the onedimensional Ising model the scalar curvature, √sinh^{2}(h) + exp(4β). This is positive definite and, for physical fields and temperatures, diverges only at the zerotemperature, zerofield 'critical point' of the model. In this paper we calculate β, h) + B(q, β, h)/√η(q, β, h), where η(q, β, h) is the Potts analogue of sinh^{2}(h) + exp(4β). This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the LeeYang edge.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2002
 DOI:
 10.1088/03054470/35/43/303
 arXiv:
 arXiv:condmat/0207180
 Bibcode:
 2002JPhA...35.9025D
 Keywords:

 Statistical Mechanics
 EPrint:
 9 pages + 4 eps figures