  Van der Waals like behavior of $f(R)$ AdS black holes is revisited via two
point correlation function, which is dual to the geodesic length in the bulk.
The equation of motion constrained by the boundary condition is solved
numerically and both the effect of boundary region size and $f(R)$ gravity are
probed. Moreover, an analogous specific heat related to $\delta L$ is
introduced. It is shown that the $T-\delta L$ graphs of $f(R)$ AdS black holes
exhibit reverse van der Waals like behavior just as the $T-S$ graphs do. Free
energy analysis is carried out to determine the first order phase transition
temperature $T_*$ and the unstable branch in $T-\delta L$ curve is removed by a
bar $T=T_*$. It is shown that the first order phase transition temperature is
the same at least to the order of $10^{-10}$ for different choices of the
parameter $b$ although the values of free energy vary with $b$. Our result
further supports the former finding that charged $f(R)$ AdS black holes behave
much like RN-AdS black holes. We also check the analogous equal area law
numerically and find that the relative errors for both the cases $\theta_0=0.1$
and $\theta_0=0.2$ are small enough. The fitting functions between $ \log\mid T
-T_c\mid$ and $\log\mid\delta L-\delta L_c\mid $ for both cases are also
obtained. It is shown that the slope is around 3, implying that the critical
exponent is about $2/3$. This result is in accordance with those in former
literatures of specific heat related to the thermal entropy or entanglement
entropy.
