Journal of Statistical Physics

, Volume 145, Issue 3, pp 696–712 | Cite as

Series Analysis of a Kosterlitz-Thouless Transition: The 6-State Planar Potts Model

Article

Abstract

A new implementation of the Finite Lattice Method of series expansion is used to derive low temperature series for the 6-state planar Potts model. This is expected to have Kosterlitz-Thouless transitions between the ordered low-temperature phase and a massless phase, and between the massless phase and a high-temperature disordered phase. In an exploratory study, we have analysed series for the order parameter to order x59. These series have proved particularly difficult to analyse and when seeking to both locate the transition and confirm the form of the Kosterlitz-Thouless transition, considerable ambiguity is found. If however the form of the Kosterlitz-Thouless transition is assumed, then the series analysis consistently indicates that the lower transition occurs at xL=0.4886(10). A more conservative analysis, which made no assumption about the nature of the transition, led to the estimate xL=0.485(8).

Keywords

Lattice statistical mechanics Potts model Planar Potts model Kosterlitz-Thouless transition Series expansion Essential singularity 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

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