On the connectivity index for lattices of nonintegral dimensionality |
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Authors: | Deepak Dhar |
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Institution: | (1) Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005 Bombay, India |
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Abstract: | 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. |
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Keywords: | Graph theory nonintegral dimension connectivity index |
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