Order, Disorder, and Jamming in a New Class of Spin Systems

Abstract

Spin systems provide a class of well-understood statistical models, from which we can derive new insights into seemingly disparate phenomena. In my thesis, I explore a new class of spin systems, in which neighboring spins must enclose an angle greater than a fixed exclusion angle Delta. This is analogous to a packing of hard spheres, in which only non-overlapping configurations are allowed. In studying this model, I aim to shed light on the phenomenon of order by disorder. Using the transfer matrix method and Monte Carlo simulation, I analyze this transition for XY spins with continuous symmetry as well as discretized ZN models. I then move to the nonequilibrium realm, to investigate whether this class of spin systems undergoes jamming. This relates to the question of why physical glasses, absent the quenched random variables that sow disorder in a spin glass, "jam" in a random state. An examination of the dynamical and geometrical properties of the candidate jammed states generated from a soft potential adds to the current understanding of vitrification and maximally random jammed states in the context of hard particles.