Abstract
We study the statistics of lattice animals on a class of hierarchical graphs whosemembers can be labeled by a set of integers , g≥1. We have shown that the animal critical behavior crucially depends on the minimal value of these parameters. For we find the usual power-law behavior, while for the associated generating function displays an essential singularity∼exp[c(tc−t)−ψ], wherec is a constant andthe exponent ψ is related to the leading correction term in the asymptotic behavior of the number of animal configurations havingN bonds, , ω = ψ/(ψ+1). We express theentropic exponent ω and the animal size exponent in terms of pertinent graph parameters.
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