  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.

High Energy Physics - Lattice