Cell Lists Method Based on Doubly Linked Lists for Monte Carlo Simulation

TL;DR

This paper introduces a cell lists method based on doubly linked lists with O(N) complexity, enabling efficient particle deletion, insertion, and nonlocal moves in Monte Carlo simulations, including reaction ensembles and polymer models.

Contribution

It presents a novel cell lists approach using doubly linked lists that efficiently handles nonlocal moves and particle updates in Monte Carlo simulations.

Findings

Achieves O(N) complexity for particle deletion and insertion.

Enables nonlocal moves in polymer Monte Carlo simulations.

Improves simulation efficiency for reaction ensembles and complex polymer moves.

Abstract

A cell lists method based on doubly linked lists and with complexity O(N) is developed for particle deletion and insertion in reaction ensemble Monte Carlo simulation. Because the random move in Metropolis algorithm can be reduced to particle deletion at old position and particle insertion at new position, so this method can be also used in Metropolis algorithm. In addition, nonlocal move, common in Monte Carlo simulation of polymers, such as kink-jump, pivot, reptation move and the retrace and regrow of chains in configurational biased Monte Carlo often cause the failure of Verlet lists method because the large displacement in these nonlocal moves will exceed Verlet cutoff radius. So we also use cell lists method based on doubly linked lists to achieve nonlocal move in this study.