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arXiv:hep-lat/9301017 · Physical review. B, Condensed matter

Low-temperature expansions for Potts models

Gyan V Bhanot, Michael J. Creutz, Uwe Glässner, Ivan Horváth A, Jan Lacki, Klaus Schilling, John D. Weckel

Published Sep 1, 1993• 24 citations
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Abstract

On simple-cubic lattices, we compute low-temperature series expansions for the energy, magnetization, and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds, respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure that enumerates states explicitly. We analyze the series with Dlog Pad\'e analysis and inhomogeneous differential approximants.

DOI
10.1103/physrevb.48.6183

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On simple-cubic lattices, we compute low-temperature series expansions for the energy, magnetization, and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds, respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure that enumerates states explicitly. We analyze the series with Dlog Pad'e analysis and inhomogeneous differential approximants.
For paper II, see ibid, vol. 27, p.1503 (1994). The finite-lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the 3-state Potts model on the simple cubic lattice to order z 43 and the high-temperature expansion of the partition function to order v 21 . We use the numerical data to show that the transition is first-order, and estimate the latent heat, the discontinuity in the magnetization, and a number of other critical parameters.
The finite-lattice method of series expansion is generalized to the q-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising (q=2) case the authors have extended the low-temperature series for the partition functions, magnetization and zero-field susceptibility to u 26 from u 20 . The high-temperature series for the zero-field partition function is extended from nu 18 to nu 22 . Subsequent analysis gives critical exponents in agreement with those from field theory.
The finite lattice method of series expansion is generalised to the qqq-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising (q=2q=2q=2) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to u26u^{26}u26 from u20u^{20}u20. The high-temperature series for the zero-field partition function is extended from v18v^{18}v18 to v22v^{22}v22. Subsequent analysis gives critical exponents in agreement with those from field theory.