Thermodynamics of a Potts-like model for a reconstructed zigzag edge in graphene nanoribbons

We construct a three-color Potts-like model for the graphene zigzag edge reconstructed with Stone-Wales carbon rings, in order to study its thermal equilibrium properties. We consider two cases which have different ground-states: the edge with non-passivated dangling carbon bonds and the edge fully passivated with hydrogen. We study the concentration of defects perturbing the ground-state configuration as a function of the temperature. The defect concentration is found to be exponentially dependent on the effective parameters that describe the model at all temperatures. Moreover, we analytically compute the domain size distribution of the defective domains and conclude that it does not have fat-tails. In an appendix, we show how the exchange parameters of the model can be estimated using density functional theory results. Such equilibrium mechanisms place a lower bound on the concentration of defects in zigzag edges, since the formation of such defects is due to non-equilibrium kinetic mechanisms.