  We present a detailed analysis of the unjamming transition in 2D frictionless
disk packings using a static correlation function that has been widely used to
study disordered systems. We show that this point-to-set (PTS) correlation
function exhibits a dominant length scale that diverges as the unjamming
transition is approached through decompression. In addition, we identify
deviations from meanfield predictions, and present detailed analysis of the
origin of non-meanfield behavior. A mean-field bulk-surface argument is
reviewed. Corrections to this argument are identified, which lead to a change
in the functional form of the critical PTS boundary size. An entropic
description of the origin of the correlations is presented, and simple rigidity
assumptions are shown to predict the functional form of the critical PTS
boundary size as a function of the pressure.
