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arXiv:hep-lat/9810029

Large-q expansion of the energy cumulants for the two-dimensional q-state Potts model

H. Arisue, Kanehito Tabata

Published Oct 14, 1998• 1 citation
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Abstract

We have calculated the large-q expansion for the energy cumulants at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the cumulants for $q \to 4_+$.

DOI
10.48550/arxiv.hep-lat/9810029

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We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn representation of the model. With this procedure, we compute directly the ordered phase partition function up to order 10 in 1/sqrt{q}. The energy cumulants at the transition can be obtained with suitable resummation and come out large for q less or around 15. As a consequence, expansions of the free energies around the transition temperature are useless for not large enough values of q. In particular the pure phase specific heats are predicted to be much larger, at q < 15, than the values extracted from current finite size scaling analysis of extrema, whereas they agree very well with recent values extracted at the transition point.