We have explained in detail why the canonical partition function ofInteracting Self Avoiding Walk (ISAW), is exactly equivalent to theconfigurational average of the weights associated with growth walks, such asthe Interacting Growth Walk (IGW), if the average is taken over the entiregenealogical tree of the walk. In this context, we have shown that it is notalways possible to factor the the density of states out of the canonicalpartition function if the local growth rule is temperature-dependent. We havepresented Monte Carlo results for IGWs on a diamond lattice in order todemonstrate that the actual set of IGW configurations available for study istemperature-dependent even though the weighted averages lead to the expectedthermodynamic behavior of Interacting Self Avoiding Walk (ISAW).
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