Numerical and Analytic Studies in Quantum Field Theory and Critical Phenomena

New York University, New York NY

Investigators

Abstract

The researchers will develop and apply new and more efficient computer algorithms for solving problems in quantum field theory (elementary-particle physics) and the statistical mechanics of phase transitions and critical phenomena (condensed-matter physics). They will then use these numerical studies to motivate new theoretical insights. The research focuses on two principal application areas: lattice spin models and field theories, including lattice gauge theories; and self-avoiding random walk. This work impacts simultaneously on several areas of physical science and applied mathematics. Lattice field theories are of direct interest in elementary-particle physics; in particular, lattice gauge theories provide our best model for the strong subnuclear interaction. Lattice spin models are employed to model phase transitions in numerous areas of condensed-matter physics and physical chemistry. The self-avoiding walk models the behavior of high-molecular-weight polymer molecules (including proteins and other biopolymers) in solution; it thus has applications in numerous areas of physics, chemistry and chemical engineering, and biophysics.