Predicted Critical Correlation Function for Three-Dimensional Phase Transitions

A new approximant is proposed for the critical correlation function $g\left(y\right)\mathrm{}$ of $y=k\xi$, where $\xi$ 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 $g\left(y\right)\mathrm{}$ is accurate to better than 0.03% everywhere for the two-dimensional Ising model. Results for the three-dimensional case are consistent with $\epsilon$-expansion and high-temperature series results.