Calculations of correlation functions for two-dimensional square ice

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Two approximation methods, the Monte Carlo method and the series expansion method, are used to calculate correlation functions, including the Kirkwood correlation function g, in two-dimensional square ice. The approximation methods are tested on the exact values of the polarization correlation function G and the self-correlation function g (o). Both approximate methods are reasonably precise and both methods give values of G and g (o) in good agreement with the exact values. Using both methods we estimate that g = 1.5 ± 0.3. Just as for three-dimensional ice this value of g is significantly smaller than G, thus supporting the assumption of dimensional similarity in the behavior of the correlation functions. Our results strongly indicate that g is a discontinuous function in the ideal ice limit as the Bjerrum fault concentration is varied. From these results, previous results for three-dimensional ice and general considerations relating g and G it is concluded that for real ice in three dimensions with a non-zero concentration of Bjerrum faults the values of g and G are both close to three.