  Dynamical linked cluster expansions are linked cluster expansions with
hopping parameter terms endowed with their own dynamics. This amounts to a
generalization from 2-point to point-link-point interactions. We develop an
associated graph theory with a generalized notion of connectivity and describe
an algorithmic generation of the new multiple-line graphs. We indicate physical
applications to spin glasses, partially annealed neural networks and SU(N)
gauge Higgs systems. In particular the new expansion technique provides the
possibility of avoiding the replica-trick in spin glasses. We consider
variational estimates for the SU(2) Higgs model of the electroweak phase
transition. The results for the transition line, obtained by dynamical linked
cluster expansions, agree quite well with corresponding high precision Monte
Carlo results.
