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    • On the connectivity index for lattices of nonintegral dimensionality

      Deepak Dhar

      Statistical Mechanics Volume 15 Issue 6 December 1980 pp 545-549

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/015/06/0545-0549

    • Keywords

       

      Graph theory; nonintegral dimension; connectivity index

    • 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.

    • Author Affiliations

       

      Deepak Dhar1

      1. Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay - 400 005, India

    • Dates

       
      Published
      December 1980
      Manuscript received
      14 August 1980

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