### Abstract

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 language | English (US) |
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Pages (from-to) | 7276-7281 |

Number of pages | 6 |

Journal | Physical Review B |

Volume | 31 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1985 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*31*(11), 7276-7281. https://doi.org/10.1103/PhysRevB.31.7276