25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

Abstract

25th-order high-temperature series are computed for a general nearest-neighbor three-dimensional Ising model with arbitrary potential on the simple cubic lattice. In particular, we consider three improved potentials characterized by suppressed leading scaling corrections. Critical exponents are extracted from high-temperature series specialized to improved potentials, obtaining $γ=1.2373(2)$, $ν=0.63012(16)$, $α=0.1096(5)$, $η=0.03639(15)$, $β=0.32653(10)$, $δ=4.7893(8)$. Moreover, biased analyses of the 25th-order series of the standard Ising model provide the estimate $Δ=0.52(3)$ for the exponent associated with the leading scaling corrections. By the same technique, we study the small-magnetization expansion of the Helmholtz free energy. The results are then applied to the construction of parametric representations of the critical equation of state, using a systematic approach based on a global stationarity condition. Accurate estimates of several universal amplitude ratios are also presented.