McKennzie-Moore relation

Both relations are supported by numerical calculations (see below and Table 4). A relation for is not known, and a naive straightforward conversion of the McKennzie-Moore relation [18] derived for regular lattices, Eq. (7), does not lead to consistent results. 

The values for gf, pf> <1 (the latter two using the numerical procedure discussed in Appendix C) shown in Fig. 5 are reported in Table 4. Within the presently available accuracy, it seems that the relation between ds and i, Eq. (21), holds. The verification of Eq. (22) is somewhat more delicate, and therefore it is crucial to determine the values of gf, Us, and (in particular) 7 as precisely as possible (this being the reason for the two methods of analysis to determine 7s discussed above). By doing this, the des Cloizeaux relation, Eq. (22), has been found to hold. Contrarily to the case of gf, a theoretical estimation for 5 is still lacking. For d-dimensional regular lattices, it is well known that 52 is given by the McKennzie-Moore relation [18], Eq. (7). Unfortunately, a naive straightforward conversion of Eq. (7) to the Sierpinski lattice does not lead to consistent results. 

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