Linked cluster expansions beyond nearest neighbour interactions: convergence and graph classes

Details Linked cluster expansions beyond nearest neighbour interactions: convergence and graph classes Linked cluster expansions beyond nearest neighbour interactions: convergence and graph classes

1996-04-24

arxiv.org/abs/hep-lat/9604021v1

Int.J.Mod.Phys. A12 (1997) 3739-3758

Physics

High Energy Physics

High Energy Physics - Lattice

20 pages, latex2e

Scientific paper

10.1142/S0217751X97001924

We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way that the classes of graphs to be considered are identical to those of the pure nearest neighbour interaction. The only change then concerns the computation of lattice imbedding numbers. All the complications that arise can be reduced to a generalization of the notion of free random walks, including hopping beyond nearest neighbour. Explicit expressions for combinatorical numbers of the latter are given. We show that under some general conditions the linked cluster expansion series have a non-vanishing radius of convergence.

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