# Polymer simulation by means of tree data-structures and a parsimonious Metropolis algorithm

## TL;DR

This paper introduces a Monte Carlo simulation approach for polymers using tree data structures and a modified Metropolis algorithm, achieving efficient scaling for large polymer systems with continuous degrees of freedom.

## Contribution

It presents a novel Monte Carlo method employing binary-tree data structures for efficient polymer simulation, extending to Lennard-Jones polymers and incorporating replica-exchange techniques.

## Key findings

- Time per Monte Carlo move scales logarithmically with polymer size
- Method successfully applied to Lennard-Jones polymers with untruncated interactions
- Replica-exchange method adapted for polymer simulations

## Abstract

We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per Monte Carlo move scales logarithmically with polymer size. We combine the method with a variant of the Metropolis algorithm and preserve this scaling for Lennard-Jones polymers with untruncated monomer-monomer interaction. We further show how the replica-exchange method can be adapted for the same purpose.