Two-dimensional lattice polymers: adaptive windows simulations

TL;DR

This paper introduces an adaptive window Wang-Landau sampling method for simulating self-avoiding lattice polymers, allowing accurate exploration of low-temperature regimes and overcoming limitations of fixed-window approaches.

Contribution

The study develops a novel adaptive window technique for Wang-Landau sampling that improves accuracy and efficiency in simulating lattice polymers, especially at low temperatures.

Findings

Successfully simulated chains up to 300 monomers.

Achieved accurate density of states in low-temperature regimes.

Eliminated border effects present in fixed-window methods.

Abstract

We report a numerical study of self-avoiding polymers on the square lattice, including an attractive potential between nonconsecutive monomers. Using Wang-Landau sampling (WLS) with adaptive windows, we obtain the density of states for chains of up to N=300 monomers and associated thermodynamic quantities. The method enables one to simulate accurately the low-temperature regime, which is virtually inaccessible using traditional methods. Instead of defining fixed energy windows, as in usual WLS, this method uses windows with boundaries that depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor $f$ is reduced, we eliminate border effects that arise in simulations using fixed windows.