Heuristic Monte Carlo Method Applied to Cooperative Motion Algorithm for Binary Lattice Fluid

TL;DR

This paper evaluates a heuristic Monte Carlo method within a cooperative motion algorithm for binary lattice fluids, demonstrating its effectiveness and consistency with established models through comparative simulations and parallel tempering techniques.

Contribution

It introduces and validates a heuristic Monte Carlo approach for 3D lattice polymers using a simplified 2D system, showing its agreement with traditional methods and exact solutions.

Findings

Critical temperature matches the exact Ising model value.

Heuristic method produces consistent energy and heat capacity results.

Parallel tempering improves low-temperature simulation reliability.

Abstract

The Cooperative Motion Algorithm is an efficient lattice method to simulate dense polymer systems and is often used with two different criteria to generate a Markov chain in the configuration space. While the first method is the well-established Metropolis algorithm, the other one is an heuristic algorithm which needs justification. As an introductory step towards justification for the 3D lattice polymers, we study a simple system which is the binary equimolar uid on a 2D triangular lattice. Since all lattice sites are occupied only selected type of motions are considered, such the vacancy movements, swapping neighboring lattice sites (Kawasaki dynamics) and cooperative loops. We compare both methods, calculating the energy as well as heat capacity as a function of temperature. The critical temperature, which was determined using the Binder cumulant, was the same for all methods with the simulation accuracy and in agreement with the exact critical temperature for the Ising model on the 2D triangular lattice. In order to achieve reliable results at low temperatures we employ the parallel tempering algorithm which enables simultaneous simulations of replicas of the system in a wide range of temperatures.