On the connectivity index for lattices of nonintegral dimensionality
- 22 Downloads
We define the connectivity indexc for an infinite graph by the requirement that to disconnect a subset of at leastV points from the rest of the graph requires the deletion of a minimum ofS(V) bonds whereS(V) ∼V (c−1)/c for largeV. For ad-dimensional hypercubical lattice withd integral,c=d. We construct explicit examples of lattices with nonintegral connectivity indexc, 1<c<∞. It is argued that the connectivity index is an important parameter determining the critical behaviour of Hamiltonians on these lattices.
KeywordsGraph theory nonintegral dimension connectivity index
Unable to display preview. Download preview PDF.
- Belavin A A and Yurishchev M A 1973Zh. Eskp. Theor. Fiz. 64 407Google Scholar
- Bollini C G and Giambiagi J J 1972Nuovo Cimento B12 20Google Scholar
- Collet P and Eckmann J P 1978A renormalization group analysis of the hierarchical model in statistical mechanics (Berlin: Springer-Verlag).Google Scholar
- Joyce G S 1972Phase transitions and critical phenomena eds. C Domb and M S Green (London, New York: Academic Press) Vol. 2Google Scholar