Influence of the boundary on the connective constant of branching structures

Hendrik Moraal

Physica A: Statistical Mechanics and its Applications, 1994, vol. 203, issue 2, 261-268

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.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:203:y:1994:i:2:p:261-268

DOI: 10.1016/0378-4371(94)90155-4

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