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Three-dimensional spin models of the Ising and XY universality classes arestudied by a combination of high-temperature expansions and Monte Carlosimulations applied to improved Hamiltonians. The critical exponents and thecritical equation of state are determined to very high precision.Comment: 7 pages, contribution to the 2nd Conference on the Exact  Renormalization Group, Roma, September 200

HIGH-PRECISION ESTIMATES OF CRITICAL QUANTITIES BY MEANS OF IMPROVED HAMILTONIANS