Dynamical linke cluster expansions: Algorithmic aspects and applications

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline an associated multiple-line graph theory involving extended notions of connectivity and indicate an algorithmic implementation of graphs. Fields of applications are SU(N) gauge Higgs systems within variational estimates, spin glasses and partially annealed neural networks. We present results for the critical line in an SU(2) gauge Higgs model for the electroweak phase transition. The results agree well with corresponding high precision Monte Carlo results.