Predicted Critical Correlation Function for Three-Dimensional Phase Transitions

A new approximant is proposed for the critical correlation function $g(y)$ of y=kξ, where ξ is the correlation length and k the wave number of an order-parameter fluctuation. The approach involves truncating the spectral function associated with the three-term Fisher-Langer approximant in a manner suggested by the requirement of a three-particle threshold. The resulting $g(y)$ is accurate to better than 0.03% everywhere for the two-dimensional Ising model. Results for the three-dimensional case are consistent with ε-expansion and high-temperature series results.