Recursive Enumeration of Clusters in General Dimension on Hypercubic Lattices

A recursive method for enumerating clusters on a hypercubic lattice in d spatial dimensions is presented from which the weak embedding constants are determined as polynomials in d. A tabulation for all clusters having no free ends is available for nb≤15, where nb is the number of bonds. As illustrated here and elsewhere, this tabulation can be used to generate many series expansions. A novel method of checking the enumeration with an algebraic calculation is presented.