An investigation of critical and noncritical correlations in model colloidal fluids

We present a study of the correlation length of a hard-core fluid with three different tail interactions, namely, the Asakura-Oosawa potential, an attractive Yukawa tail, and a double Yukawa tail which is attractive at short distance and repulsive at long distance. The correlation length is obtained along the critical isochore in the whole range of supercritical temperatures by determining the leading pole of the structure factor S(k) in the complex plane, where S(k) is obtained from the hierarchical reference theory. We focus on how the correlation length changes from its Ornstein-Zernike form in the critical region to its high-temperature limit, and find instances of both the Fisher-Widom and Kirkwood scenarios for the monotonic to oscillatory crossover of the decay of correlations at long distance.