  A field theory of frictionless grain packings in two dimensions is shown to
exhibit a zero-temperature critical point at a non-zero value of the packing
fraction. The zero-temperature constraint of force-balance plays a crucial role
in determining the nature of the transition. Two order parameters, <z>, the
deviation of the average number of contacts from the isostatic value and, <F>,
the average magnitude of the force per contact, characterize the transition
from the jammed (high packing fraction) to the unjammed (low packing fraction
state). The critical point has a mixed character with the order parameters
showing a jump discontinuity but with fluctuations of the contact force
diverging. At the critical point, the distribution of F shows the
characteristic plateau observed in static granular piles. The theory makes
falsifiable predictions about the spatial fluctuations of the contact forces.
Implications for finite temperature dynamics and generalizations to frictional
packings and higher dimensions are discussed
