A review of Monte Carlo simulations of polymers with PERM

TL;DR

This review discusses the application of the PERM Monte Carlo algorithm to various polymer physics problems, highlighting its advantages, limitations, and strategies for reliable results in complex systems.

Contribution

It provides a comprehensive overview of PERM's use in polymer simulations, including new insights into bias control and reliability assessment.

Findings

PERM effectively samples diverse polymer configurations.

Bias management is crucial for accurate Monte Carlo simulations.

PERM is often the preferred method for complex polymer systems.

Abstract

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the $\Theta$ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -- as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.