A particle-based Ising model

TL;DR

This paper models a 2D lattice system with particles connected by double-well potentials, showing it behaves like an Ising model and analyzing its relaxation dynamics through simulations.

Contribution

It introduces a particle-based Ising model with detailed interaction potentials and characterizes its equilibrium and coarsening behavior.

Findings

Equilibrium properties match a 2D Ising model with suitable coupling.

Cluster growth over time aligns with Monte Carlo simulation results.

System relaxation dynamics are effectively captured by the proposed model.

Abstract

We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with respect to the lattice plane and interact with each other through a Lennard-Jones potential truncated at the nearest neighbor distance. We show that the system's equilibrium properties are accurately described by a two-dimensional Ising model with an appropriate coupling constant. Moreover, we characterize the coarsening kinetics by calculating the cluster size as a function of time and compare the results with Monte Carlo simulations based on Glauber or reactive dynamics rate constants.