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

量子场论和临界现象的新的计算算法蒙特卡罗模拟在高能物理、凝聚态物理和聚合物物理中非常重要，特别是在相互作用强且分析方法不可用的领域。然而，大多数蒙特卡罗算法在相关函数开始发散的“临界点”附近变得效率低下。需要克服的现象被称为“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中的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回避随机行走的蒙特卡罗算法。算法策略将采用基于启发式物理推理和严格数学分析相结合的集体模式(多尺度)更新。

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.