Static properties of 2D spin-ice as a sixteen-vertex model
  We present a thorough study of the static properties of 2D models of spin-ice type on the square lattice or, in other words, the sixteen-vertex model. We use extensive Monte Carlo simulations to determine the phase diagram and critical properties of the finite dimensional system. We put forward a suitable mean-field approximation, by defining the model on carefully chosen trees. We employ the cavity (Bethe-Peierls) method to derive self-consistent equations, the fixed points of which yield the equilibrium properties of the model on the tree-like graph. We compare mean-field and finite dimensional results. We discuss our findings in the context of experiments in artificial two dimensional spin ice. 
Laura Foini, Demian Levis, Marco Tarzia and Leticia F. Cugliandolo
cond-mat.stat-mech