Dynamical linked cluster expansions: A novel expansion scheme for point-link-point interactions

Dynamical linked cluster expansions are linked cluster expansions with hopp ing parameter terms endowed with their own dynamics. This amounts to a gene ralization from two-point to point-link-point interactions. We develop an a ssociated graph theory with a generalized notion of connectivity and descri be an algorithmic generation of the new multiple-line graphs. We indicate p hysical applications to spin glasses, partially annealed neural networks an d SU(N) gauge Higgs systems. In particular the new expansion technique prov ides the possibility of avoiding the replica trick in spin glasses. We cons ider variational estimates for the SU(2) Higgs model of the electroweak pha se transition. The results for the transition line, obtained by dynamical l inked cluster expansions, agree quite well with corresponding high precisio n Monte Carlo results.