D S Gaunt et al 1980 J. Phys. A: Math. Gen. 13 1791 doi:10.1088/0305-4470/13/5/037
D S Gaunt, J L Martin, G Ord, G M Torrie and S G Whittington
Show affiliationsExact values of the numbers of connected clusters of n sites, each site having valence no larger than nu , are presented for the simple cubic lattice for nu =2, 3, 4, 5 and 6 for small values of n. Assuming a plausible asymptotic form for the dependence of these numbers on n and nu the authors show rigorously that the exponent tau characterising the dominant singularity in the generating function is negative for nu =2 but positive for nu >or=3. Series analysis techniques suggest that the same value of tau obtains for all nu >or=3.
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 5 (1 May 1980)
D S Gaunt et al 1980 J. Phys. A: Math. Gen. 13 1791
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