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We propose a method to obtain an improved Hamiltonian (action) for the Isinguniversality class in three dimensions. The improved Hamiltonian has suppressedleading corrections to scaling. It is obtained by tuning models with twocoupling constants. We studied three different models: the +1,-1 Ising modelwith nearest neighbour and body diagonal interaction, the spin-1 model withstates 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on thelattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scalingproperties of the suitably tuned spin-1 model are compared in detail with thoseof the standard Ising model. Great care is taken to estimate the systematicerrors from residual corrections to scaling. Our best estimates for thecritical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given errorestimates take into account the statistical and systematic uncertainties.Comment: 55 pages, 12 figure

Critical exponents of the three-dimensional Ising universality class from finite-size scaling with standard and improved actions