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

  • I. G. Enting
  • N. Clisby


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 x 59. 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 x L=0.4886(10). A more conservative analysis, which made no assumption about the nature of the transition, led to the estimate x L=0.485(8).


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


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Authors and Affiliations

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

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