  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.
