Dolan, Brian P. and Johnston, D.A. and Kenna, R. (2002) The Information Geometry of the OneDimensional Potts Model. Journal of Physics A: Mathematical and General, 35 (43). pp. 90259036.
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Abstract
In various statisticalmechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, 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, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp ( 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zerotemperature, zerofield ``critical point'' of the model. In this note we calculate ${\cal R}$ for the onedimensional $q$state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp ( 4 \beta)$. 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.
Item Type:  Article 

Keywords:  Renormalisation group, chaos 
Academic Unit:  Faculty of Science and Engineering > Experimental Physics 
Item ID:  268 
Depositing User:  Dr. Brian Dolan 
Date Deposited:  09 Nov 2005 
Journal or Publication Title:  Journal of Physics A: Mathematical and General 
Publisher:  Institute of Physics 
Refereed:  Yes 
URI: 
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