Domain Coarsening Within the Ising Model on the Hyperbolic Plane*

In spite of its simplicity, both the dynamics and equilibrium statistics of the Ising model are nontrivial. Previous studies in this REU have shown that the dynamics of metastable decay is very different in the hyperbolic plane than in the Euclidean plane. Here we perform Monte Carlo simulations of domain coarsening in the hyperbolic plane. We find that domain coarsening occurs more slowly than in the Euclidean plane.