Rigorous studies of critical behavior

Presented here are some basic results on the phase structure and the critical behavior in general classes of translation invariant ferromagnetic systems, and in independent percolation models. Some of these results were derived by means of nonlinear partial differential inequalities involving the order parameter. While the inequalities are satisfied in the discrete lattice systems, their structure contains hints of relations with suitable field theories (“φ4” for ferromagnetic systems, and “φ3” in case of percolation).