Inverse statistical mechanics, lattice packings, and glasses

Computer simulation methods enable the investigation of systems and properties that are intractable by purely analytical or experimental approaches. Each chapter of this dissertation contains an application of simulation methods to solve complex physical problems consisting of interacting many-particle or many-spin systems. The problems studied in this dissertation can be divided up into the following two broad categories: inverse and forward problems.;The inverse problems considered are those in which we construct an interaction potential such that the corresponding ground state is a targeted configuration. In Chapters 2 and 3, we devise convex pair-potential functions that result in low-coordinated ground states. Chapter 2 describes targeted ground states that are the square and honeycomb crystals, while in Chapter 3 the targeted ground state is the diamond crystal. Chapter 4 applies similar techniques to explicitly enumerate all unique ground states up to a given system size, for spin configurations that interact according to generalized isotropic Ising potentials with finite range.;We also consider forward statistical-mechanical problems. In Chapter 5, we adapt a linear programming algorithm to find the densest lattice packings across Euclidean space dimensions. In Chapter 6, we demonstrate that for two different glass models a signature of the glass transition is apparent well before the transition temperature is reached. In both models, this signature appears as nonequilibrium length scales that grow upon supercooling.