Cavity method for jammed disordered packings of hard particles at mean-field level

We apply the cavity method at mean-field level to investigate the problem of random close packings of hard particles. We derive the Belief Propagation equations describing this force/torque balance problem to solve the force distribution and suggest an estimation of the coordination number of the jammed packing. We compare the numerical results with approximate analytical solutions and show the dependence of coordination numbers on particle shapes. The method can be applied to spherical frictionless and frictional particles as well as non-spherical particles to obtain the jamming properties and study the appearance of isostaticity.