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

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 u²⁶ from u²⁰. 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.