| In this dissertation, the ground and excited states associated with three families of particle interactions in classical interacting many-particle systems are examined. In each part, the choice for a family of interactions is motivated and the low-temperature behaviors are analyzed using computational methods. The research presented herein is discussed in the context of recent experimental advances.;In Part I, we examine soft pair interactions v( r) that possess a Fourier transform V(k ) that is positive and has compact support at wave number K. Using these "collective-coordinate" potentials and numerical optimization, we construct ground states so that the scattering of radiation exactly matches a prescribed pattern for a set of wave vectors. "Stealth" materials, which suppress scattering at certain wavelengths, are counterintuitively disordered in the infinite-volume limit. We also design "equi-luminous" materials, which scatter radiation equally intensely for a set of wave vectors. With a model V(k), we attribute unusual low-temperature behaviors to the topography of the energy landscape. The thermodynamic and structural properties of inherent structures are analyzed and connected to the features of the energy landscape above the ground state. These point patterns can be used as the basis for novel materials.;In Part II, we introduce the "quintic potential" to stabilize vacancy-riddled triangular lattices as ground states. Using numerical methods, we identify high-density and low-density triangular lattices, kagome and honeycomb crystals, and stripes as ground states. These structures have stable phonon modes but are difficult to self-assemble in simulations. Two special regimes are identified and discussed.;In Part III, we construct the phase diagram of hard superballs using molecular dynamics in a deformable simulation box for the interpolation between spheres and cubes. Asphericity plays a significant role in the the extent of cubatic ordering in liquid and crystal phases. Superballs similar to cubes maintain long-ranged orientational order upon the reduction of density. Systems are characterized using order parameters and correlation functions. We also find that fixed simulation cells induce artificial phase transitions. |
