Mathematical Sciences: Constructive Computer Methods Appliedto Problems in Statistical Mechanics and Quantum Field Theory

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This research project plans to combine a number of computer-assisted methods developed by the PI and others and construct the renormalization group fixed point which governs the infrared behavior of critical lattice systems in three dimensions, such as the critical phi 4/3 scalar quantum field model or the three dimensional Ising model. It also plans to get rigorous bounds on the (universal) critical exponents of these models. The work to get the rigorous results for these three dimensional models will be done on a supercomputer. Quantum field theory is aimed at a rigorous mathematical construct for quantum physical models of reality. Conclusions deduced from the theory will enhance our understanding of quantum physics and allow us to exploit this new understanding for new and innovative technological advances.