Do dipole correlations exist in two-dimensional spin ice?
  Here we study the statistical properties of two-dimensional spin ice in its ground state by the Monte Carlo simulation method. Using a new sampling algorithm, we show that the short-range ice rule in two dimensions gives rise to long-range but not dipole-like correlations, to non-Gaussian probability density function for magnetization and to non-extensive conditional entropy (entropy with given value of magnetization). 
M. I. Ryzhkin
cond-mat.stat-mech cond-mat.str-el