What does the g(r) look like near the critical point?
I know what the pair correlation function (radial distribution function) should look like for a solid, which has regular packing and therefore the g(r) will not decay with time. And I know what it looks like for, say, a dense Lennard-Jones fluid. But I don't know what it will look like near the critical point, where the correlation length diverges.
I found here a figure that shows the g(r) for a Lenanrd-Jones fluid in the critical region. It appears that the initial peak is lower than the initial peak of g(r) near the triple point and that it then attenuates to zero rather quickly, without any of the normal lesser peaks. How does this show that the correlation length diverges?