Series studies of the Potts model. I: The simple cubic Ising model

Details Series studies of the Potts model. I: The simple cubic Ising model Series studies of the Potts model. I: The simple cubic Ising model

1992-12-24

arxiv.org/abs/hep-lat/9212032v1

J.Phys.A26:807-822,1993

Physics

High Energy Physics

High Energy Physics - Lattice

submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 pages

Scientific paper

10.1088/0305-4470/26/4/010

The finite lattice method of series expansion is generalised 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 we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. Subsequent analysis gives critical exponents in agreement with those from field theory.

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