A growth walk model for estimating the canonical partition function of Interacting Self Avoiding Walk

TL;DR

This paper demonstrates that the canonical partition function of Interacting Self Avoiding Walks can be estimated using growth walk models, with Monte Carlo results validating the approach despite temperature-dependent growth rules.

Contribution

It introduces a growth walk model for estimating the ISAW partition function and analyzes the impact of temperature-dependent growth rules on configurational sampling.

Findings

Partition function equals configurational average of growth walk weights.

Temperature dependence affects the set of accessible configurations.

Monte Carlo simulations confirm thermodynamic behavior of ISAW.

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).