Dispersion Theory Approach for the Critical Correlation Function

A one-parameter scaling function $s(x)$ of x=kξ, where ξ is the correlation length and k the wave number of a density or concentration fluctuations in a fluid, is derived from a phenomenological field theoretic approach. On the basis of a positive-definite spectral function, we exploit the requirements of a three-particle threshold and the correct asymptotic approach as x→∞. The resulting $s(x)$ is compared with the Fisher-Burford approximant obtained from numerical studies of the three-dimensional Ising model.