Lattice Models and Applications

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9980440WuThis grant supports theoretical research on the statistical mechanics of lattice models. It is supported by the Divisions of Materials Research and Mathematical Sciences. Lattice models play an essential role in the modern theory of critical phenomena, which finds wide applications in physics, materials research and other disciplines including engineering and mathematics. This research involves theoretical studies of lattice models with emphases on exact and rigorous results and their applications.Exact analyses of lattice models have been restricted in the past mostly to systems in two dimensions. This project proposes to study 3-dimensional systems relevant to real physics. The study of a directed percolation model in three dimensions will also be conducted. In addition, investigation of 2-dimensional systems will be carried out including: the Ising model; dimer statistics; Fisher zeroes of the Potts model; quantum spin systems; applications to crystal surfaces; and, applications in mathematics.%%%This grant supports theoretical research on the statistical mechanics of lattice models. It is supported by the Divisions of Materials Research and Mathematical Sciences. Lattice models play an essential role in the modern theory of critical phenomena, which finds wide applications in physics, materials research and other disciplines including engineering and mathematics. This research involves theoretical studies of lattice models with emphases on exact and rigorous results and their applications.***