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Influence of the boundary on the connective constant of branching structures

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  • Moraal, Hendrik

Abstract

It is shown that the connective constant of a branching structure is modified if account is taken of the presence of a boundary containing a finite fraction of the vertices of the system. In particular, for a Cayley branch with branching ratio m, the calculation of the self-avoiding walk generating function shows that the connective constant is μ = m, whereas the corresponding Bethe lattice result is μ = m. As a second example, a triangular cactus tree is studied, giving μ = 12(42 + 2 +2) in contrast to the value μ = 1 + 3 for the corresponding infinite graph.

Suggested Citation

  • Moraal, Hendrik, 1994. "Influence of the boundary on the connective constant of branching structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 203(2), pages 261-268.
    • Handle: RePEc:eee:phsmap:v:203:y:1994:i:2:p:261-268
    DOI: 10.1016/0378-4371(94)90155-4
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