Theory of defects in hard core statistical ensembles

Systems of particles are considered which interact only via their disk-shaped hard core. By use of the single occupancy model developed by Hoover and Ree we integrate out those degrees of freedom where the centers of particles are confined to “Wigner-Seitz” cells. In contrast to Hoover and Ree the auxiliary system of Wigner-Seitz cells is taken nonrigid and described by a set of vertex coordinates“ηp”. The decimation procedure of degrees of freedom over the Wigner-Seitz cells leaves then the partition function defined in terms of the Boltzmann factor exp(δS(“eta;p”)/kB). Via the “interaction” function—TδS(“ηp”) all the usual solid state properties are defined, e.g., elastic properties, phonon excitations and defects. This theory allows then a derivation of the positional correlation function which is done in the “harmonic” approximation for the solid and molten phase. The directional correlation function is discussed in terms of domains and their respective coincidence boundary system, and disclinations.