A growth walk model for estimating the canonical partition function of Interacting Self Avoiding Walk
Abstract
We have explained in detail why the canonical partition function of Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the configurational average of the weights associated with growth walks, such as the Interacting Growth Walk (IGW), if the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the the density of states out of the canonical partition function if the local growth rule is temperature-dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature-dependent even though the weighted averages lead to the expected thermodynamic behavior of Interacting Self Avoiding Walk (ISAW).
Keywords
Cite
@article{arxiv.0706.0065,
title = {A growth walk model for estimating the canonical partition function of Interacting Self Avoiding Walk},
author = {S. L. Narasimhan and P. S. R. Krishna and M. Ponmurugan and K. P. N. Murthy},
journal= {arXiv preprint arXiv:0706.0065},
year = {2009}
}
Comments
Revised version consisting of 12 pages (RevTeX manuscript, plus three .eps figure files); A few sentences in the second paragraph on Page 4 are rewritten so as to make the definition of the genealogical tree, ${\cal Z}_N$, clearer. Also, the second equality of Eq.(1) on Page 4, and its corresponding statement below have been removed