title: (2+1)-Dimensional directed polymer in a random medium: scaling phenomena and universal distributions.
abstract: We examine numerically the zero-temperature (2+1)-dimensional directed polymer in a random medium, along with several of its brethren via the Kardar-Parisi-Zhang (KPZ) equation. Using finite-size and KPZ scaling Ansätze, we extract the universal distributions controlling fluctuation phenomena in this canonical model of nonequilibrium statistical mechanics. Specifically, we study point-point, point-line, and point-plane directed polymer geometries, scenarios which yield higher-dimensional analogs of the Tracy-Widom distributions of random matrix theory. Our analysis represents a robust, multifaceted numerical characterization of the 2+1 KPZ universality class and its limit distributions.
authors.affiliation: Physics Department, Barnard College, Columbia University, New York, New York 10027, USA.
authors.forename: Timothy
authors.initials: T
authors.lastname: Halpin-Healy