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Quantum Monte Carlo and semiclassical methods are used to solve two and foursite cluster dynamical mean field approximations to the square lattice Hubbardmodel at half filling and strong coupling. The energy, spin correlationfunction, phase boundary and electron spectral function are computed andcompared to available exact results. The comparision permits a quantitativeassessment of the ability of the different methods to capture the effects ofintersite spin correlations. Two real space methods and one momentum spacerepresentation are investigated. One of the two real space methods is found tobe significantly worse: in it, convergence to the correct results is found tobe slow and, for the spectral function, nonuniform in frequency, withunphysical midgap states appearing. Analytical arguments are presented showingthat the discrepancy arises because the method does not respect the polestructure of the self energy of the insulator. Of the other two methods, themomentum space representation is found to provide the better approximation tothe intersite terms in the energy but neither approximation is particularlyacccurate and the convergence of the momentum space method is not uniform. Afew remarks on numerical methods are made.Comment: Errors in previous versions corrected; CDMFT results adde

Fictive-impurity approach to dynamical mean-field theory: A strong-coupling investigation