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Force distribution in frictionless granular packings at rigidity threshold

With a new simulation method, involving viscous lubricating forces, we identify the exact list of active contacts in a model two-dimensional frictionless granular packing at equilibrium under an isotropic load. Within a well-justified approximation of infinitesimal displacements, efforts are localized on a minimal central-force structure that satisfies a geometric optimization criterion. Size and boundary effects are analysed. The maximum packing density of discs is evaluated to first order in their small polydispersity parameter. We find no diverging correlation length in the thermodynamic limit, and accurately compute the distribution of contact forces in large systems.