Dynamical Linked Cluster Expansions for Spin Glasses

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. An associated graph theory with a generalized notion of connectivity is reviewed. We discuss physical applications to disordered systems, in particular to spin glasses, such as the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n = 0, that usually goes along with an application of the replica trick. Invited contribution to RECENT RESEARCH DEVELOPMENTS IN STATSTICAL PHYSICS, ed. by Transworld Research Network E-mail address: [email protected] 3 E-mail address: [email protected], supported by a Heisenberg Fellowship