Inverse Statistical Mechanics, Lattice Packings, and Glasses

Abstract

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.