Numerical and Analytic Studies in Quantum Field Theory and Critical Phenomena

研究人员将开发和应用新的、更有效的计算机算法来解决量子场论(基本粒子物理)和相变统计力学和临界现象(凝聚态物理)中的问题。然后，他们将利用这些数值研究来激发新的理论见解。这项研究集中在两个主要的应用领域：格子自旋模型和场论，包括格子规范理论；以及自避免随机游动。这项工作同时影响到物理科学和应用数学的几个领域。晶格场理论直接涉及基本粒子物理，特别是晶格规范理论为强亚核相互作用提供了最好的模型。晶格自旋模型被用来模拟凝聚态物理和物理化学中的许多领域的相变。自回避行走模型模拟了高分子量聚合物分子(包括蛋白质和其他生物聚合物)在溶液中的行为，因此在物理、化学和化学工程以及生物物理的许多领域都有应用。

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.