Efficiency of Rejection-Free Methods for Dynamic Monte Carlo Studies of Off-lattice Interacting Particles

TL;DR

This paper evaluates the efficiency of a rejection-free dynamic Monte Carlo method for off-lattice particles with repulsive power-law interactions, deriving theoretical efficiency formulas and confirming them through simulations across multiple dimensions.

Contribution

It provides a theoretical analysis of the algorithm's efficiency at low temperatures and high densities, validated by comprehensive simulations in various dimensions.

Findings

Efficiency scales as rac{rac{p+2}{2}}{rac{d}{2}} with density and temperature.

Simulation results agree with theoretical predictions across dimensions.

Method is effective for studying off-lattice interacting particles at different conditions.

Abstract

We calculate the efficiency of a rejection-free dynamic Monte Carlo method for $d$-dimensional off-lattice homogeneous particles interacting through a repulsive power-law potential $r^{-p}$. Theoretically we find the algorithmic efficiency in the limit of low temperatures and/or high densities is asymptotically proportional to $\rho^{\tfrac{p+2}{2}}T^{-\tfrac{d}{2}}$ with the particle density $\rho$ and the temperature $T$. Dynamic Monte Carlo simulations are performed in 1-, 2- and 3-dimensional systems with different powers $p$, and the results agree with the theoretical predictions.