An interdisciplinary research group will be established at New York University devoted to the development of new numerical methods for the study of quantum field theory (primarily lattice gauge theories) and critical phenomena. The group will consist initially of Professors Jonathan Goodman, Alan Sokal and Daniel Zwanziger, a post-doctoral fellow, and two graduate students. A special strength of the group will be the cross-fertilization between the three disciplines represented by the researchers: numerical analysis, quantum field theory, and statistical mechanics. This collaboration has led to the development of the multi-grid Monte Carlo method, which shows great promise for radically improving the efficiency of Monte Carlo method. The major project of the group will be to continue the investigation of this method. A second project will be to develop new algorithms for computing the fermion propagator in a background gauge field; this is a key step in numerical studies of lattice gauge theory with fermions. In addition, the group plans to continue its investigations of algorithms for dynamical fermions, for the random-resistor problem, and for the self- avoiding random walk.
