Effective-medium theory of percolation on central-force elastic networks. II. Further results

E. J. Garboczi, M. F. Thorpe

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The effective-medium theory developed in a previous paper for elastic networks with a fraction p of the bonds present is extended to networks which have central forces of arbitrary range. The results are illustrated by studying a square lattice with a fraction p1 of nearest-neighbor bonds present and a fraction p2 of next-nearest-neighbor bonds present. We show that effective-medium theory gives an excellent description of the elastic properties of the networks. An argument using constraints is used to show that the network loses its elastic properties when p1+p2<1 and that the number of zero-frequency modes depends only on p1+p2. We construct flow diagrams to show that a line of fixed points exists when p1+p2=1, along which the ratio of elastic constants attains a universal value that depends on p1 but not on the spring constants. The simulations show no significant deviations from the effective-medium results.

Original languageEnglish (US)
Pages (from-to)7276-7281
Number of pages6
JournalPhysical Review B
Issue number11
StatePublished - Jan 1 1985

ASJC Scopus subject areas

  • Condensed Matter Physics


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