The Rubber Band Revisited: Wang-Landau Simulation

TL;DR

This paper applies an improved Wang-Landau simulation method to a 2D homopolymer model, demonstrating enhanced accuracy in estimating thermodynamic properties by updating the density of states after every N moves, and validating results against exact solutions.

Contribution

It introduces an optimized updating scheme for Wang-Landau sampling in polymer models, improving precision in thermodynamic calculations compared to previous methods.

Findings

Updated density of states improves simulation accuracy

Specific heat peaks match exact solutions

Method effective across different polymer constraints

Abstract

In this work we apply Wang-Landau simulations to a simple model which has exact solutions both in the microcanonical and canonical formalisms. The simulations were carried out by using an updated version of the Wang-Landau sampling. We consider a homopolymer chain consisting of $N$ monomers units which may assume any configuration on the two-dimensional lattice. By imposing constraints to the moves of the polymers we obtain three different models. Our results show that updating the density of states only after every $N$ monomers moves leads to a better precision. We obtain the specific heat and the end-to-end distance per monomer and test the precision of our simulations comparing the location of the maximum of the specific heat with the exact results for the three types of walks.