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.
