Cluster algorithm for Monte Carlo simulations of spin ice

We present an algorithm for Monte Carlo simulations of a nearest-neighbor spin-ice model based on its cluster representation. To assess its performance, we estimate a relaxation time, and find that, in contrast to theMetropolis algorithm, our algorithm does not develop spin freezing. Also, to demonstrate the efficiency, we calculate the spin and charge structure factors, and observe pinch points in a high-resolution color map. We then find that Debye screening works among defects and brings about short-range correlations, and that the deconfinement transition triggered by a fugacity of defects z is dictated by a singular part of the free-energy density f(s) alpha z