This proposal requests the support of theoretical studies of the phenomena of order-disorder transitions. Emphases of this research program are placed on obtaining exact and rigorous results. Specific problems proposed for study include graphical approach to lattice-statistical problems, the antiferromagnetic Potts model, the Blume-Emery-Griffiths model, directed percolation, the axial-next-nearest-neighbor spin models, the writing a review on the subject of the vertex model, and rigorous entropy bounds in spin systems.
