Dynamical linked cluster expansions: Algorithmic aspects and applications

Dynamical linked cluster expansions are linked cluster expansions with hopp ing parameter terms endowed with their own dynamics. They amount to a gener alization of series expansions from 2-point to point-link-point interaction s. We outline an associated multiple-line graph theory involving extended n otions of connectivity and indicate an algorithmic implementation of graphs . Fields of applications are SU(N) gauge Higgs systems within variational e stimates, spin glasses and partially annealed neural networks. We present r esults for the critical line in an SU(2) gauge Higgs model for the electrow eak phase transition. The results agree well with corresponding high precis ion Monte Carlo results.