Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

High-temperature series are computed for a generalized three-dimensional Ising model with arbitrary potential. Three specific "improved" potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are gamma = 1.2371(4), nu = 0.63002(23), alpha = 0.1099(7), eta = 0.0364(4), beta = 0.32648(18). By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented. [S1063-651X(99)09409-X].