Numerical and Analytic Studies in Quantum Field Theory and Critical Phenomena

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The researchers will develop and apply new and more efficientcomputer algorithms for solving problems in quantum field theory(elementary-particle physics) and the statistical mechanics ofphase transitions and critical phenomena (condensed-matter physics).They will then use these numerical studies to motivate new theoreticalinsights. 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 scienceand applied mathematics. Lattice field theories are of direct interestin elementary-particle physics; in particular, lattice gauge theoriesprovide our best model for the strong subnuclear interaction.Lattice spin models are employed to model phase transitionsin numerous areas of condensed-matter physics and physical chemistry.The self-avoiding walk models the behavior of high-molecular-weightpolymer molecules (including proteins and other biopolymers) in solution;it thus has applications in numerous areas of physics, chemistry andchemical engineering, and biophysics.