Interactions leading to disordered ground states and unusual low-temperature behavior

We have shown that any pair potential function v(r) possessing a Fourier transform V(k) that is positive and has compact support at some finite wave number K yields classical disordered ground states for a broad density range [R. D. Batten, F. H. Stillinger, and S. Torquato, J. Appl. Phys. 104, 033504 (2008)]. By tuning a constraint parameter chi (defined in the text), the ground states can traverse varying degrees of local order from fully disordered to crystalline ground states. Here, we show that in two dimensions, the "k-space overlap potential," where V(k) is proportional to the intersection area between two disks of diameter K whose centers are separated by k, yields anomalous low-temperature behavior, which we attribute to the topography of the underlying energy landscape. At T = 0, for the range of densities considered, we show that there is continuous energy degeneracy among Bravais-lattice configurations. The shear elastic constant of ground-state Bravais-lattice configurations vanishes. In the harmonic regime, a significant fraction of the normal modes for both amorphous and Bravais-lattice ground states have vanishing frequencies, indicating the lack of an internal restoring force. Using molecular-dynamics simulations, we observe negative thermal-expansion behavior at low temperatures, where upon heating at constant pressure, the system goes through a density maximum. For all temperatures, isothermal compression reduces the local structure of the system unlike typical single-component systems.