ITR-ASE-sim: New Computational Algorithms for Quantum Field Theory and Critical Phenomena

ITR-ASE-sim：量子场论和临界现象的新计算算法

• 批准号: 0424082
• 负责人: Alan Sokal
• 金额: $ 129.82万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0424082&HistoricalAwards=false
• 关键词: ITR; ASE; sim; New; Computational

New Computational Algorithms for Quantum Field Theory and Critical Phenomena Monte Carlo simulations are very important in high-energy physics, condensed matter physics and polymer physics especially in domains where interactions are strong and analytically methods are not available. However most Monte Carlo algorithms become inefficient near "critical points" where correlation functions start diverging. The phenomena to be overcome is called "critical slowing down". The objective of this project is to develop new and more efficient computational algorithms for problems in quantum field theory and the statistical mechanics of critical phenomena. Two general types of algorithms will be developed: Monte Carlo algorithms for simulating lattice field theories and spin models and Monte Carlo algorithms for simulating self-avoiding random walks. The algorithmic strategy will be to employ collective mode (multi-scale) updates based on a combination of heuristic physical reasoning and rigorous mathematical analyses.

量子场论和临界现象的新计算算法蒙特卡罗模拟在高能物理、凝聚态物理和高分子物理中非常重要，尤其是在相互作用很强且无法使用解析方法的领域。然而，大多数蒙特卡罗算法在相关函数开始发散的“临界点”附近变得低效。要克服的现象称为“临界减速”。这个项目的目标是为量子场论和临界现象的统计力学问题开发新的和更有效的计算算法。将开发两种一般类型的算法：用于模拟晶格场理论和自旋模型的蒙特卡罗算法和用于模拟自避免随机行走的蒙特卡罗算法。算法战略将采用集体模式（多尺度）更新的基础上结合启发式物理推理和严格的数学分析。