Geoffrey Grimmett Abstra t. Known differential inequalities for certain ferromagnetic Potts models with pairinteractions may be extended to Potts models with many-body interactions. As a major application of such differential inequalities, we obtain necessary and sufficient conditions on the set of interactions of such a Potts model in order that its critical point be a strictly monotonic funct...

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations motion Newtonian type (“acceleration equals forces”) which determine the points in complex plane. These models solvable, namely their configuration at any time can be obtained from initial data algebraic operations, amounting to determination zeros a known time-dependent polynomia...