Mathematical Sciences: Order and Disorder in Spatially Distributed Systems

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This research is concerned with phase transitions and critical phenomena. The principal investigator, in collaboration with D. Abraham, recently introduced and exactly soluble model of three dimensional wetting; they plan to study some of the remaining open problems in this random surface model including the issue of surface roughening. Professor Newman proposes to extend his joint work on percolation in half spaces with D. Barsky and G. Grimmett, in order to prove continuity of the percolation transition in full spaces. He also intends to study with C. Wu related problems in inverse square models. Professor Newman plans to investigate the use of percolation theoretic methods, which have been very fruitful in the study of ferromagnetic phase transitions, for the analysis of short range spin glasses.