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.
Download (289kB)

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:  
Use Licence:  This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BYNCSA). Details of this licence are available here 
Repository Staff Only(login required)
Item control page 
Downloads
Downloads per month over past year