  The recently introduced nested sampling algorithm allows the direct and
efficient calculation of the partition function of atomistic systems. We
demonstrate its applicability to condensed phase systems with periodic boundary
conditions by studying the three dimensional hard sphere model. Having obtained
the partition function, we show how easy it is to calculate the compressibility
and the free energy as functions of the packing fraction and local order,
verifying that the transition to crystallinity has a very small barrier, and
that the entropic contribution of jammed states to the free energy is
negligible for packing fractions above the phase transition. We quantify the
previously proposed schematic phase diagram and estimate the extent of the
region of jammed states. We find that within our samples, the maximally random
jammed configuration is surprisingly disordered.
