  Linked cluster expansions provide a useful tool for both analytical and
numerical investigations of lattice field theories. The expansion parameter(s)
being the interaction strength(s) fields at neighboured lattice sites are
coupled, they result into convergent hopping parameter like series for free
energies, correlation functions and in particular susceptibilities. We consider
scalar fields with O(N) symmetric nearest neighbour interactions on hypercubic
lattices with possibly finite extension in some directions, thus including
field theories at finite temperature T. We improve known and develop new
techniques and algorithms to increase the order n the expansions can be
computed to in such a way that detailed information on critical behaviour can
be extracted from the susceptibility series. This concerns both simple moments
as well as higher correlations such as 4- and 6-point functions used to define
renormalized coupling constants. Particular emphasis is done on finite
temperature field theory. In order to be able to measure finite T critical
behaviour, the order of explicit computation n has to be sufficiently large
compared to 1/T in lattice units. 2- and 4-point susc. series are computed up
to and including the 18th order and beyond.
