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We have compared the results of our approximation scheme, the composite operator method, for the double occupancy and the internal energy of the two-dimensional Hubbard model with numerical data obtained by means of the Lanczos and quantum Monte Carlo schemes. The agreement is very good at both half-filling and away from it showing how reliable is the approximation scheme.doi:10.1142/s0217979203016224 fatcat:ay46txosiffmpcko2vfofnger4