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

We compute an improved action for the Ising universality class in three dimensions that has suppressed leading corrections to scaling. It is obtained by tuning models with two coupling constants. We studied three different models: the $\pm 1$ Ising model with nearest-neighbor and body diagonal interaction, the spin-1 model with states $0,\pm 1$, and nearest-neighbor interaction, and ${\phi }^4$ theory on the lattice (Landau-Ginzburg model). The remarkable finite-size scaling properties of the suitably tuned spin-1 model are compared in detail with those of the standard Ising model. Great care is taken to estimate the systematic errors from residual corrections to scaling. Our best estimates for the critical exponents are $\nu =0.6298\mathrm{}\left(5\right)\mathrm{}$ and $\eta =0.0366\mathrm{}\left(8\right)\mathrm{}$, where the given error estimates take into account the statistical and systematic uncertainties.