On minimal/maximal ground-state thresholds in uniform classes of 2D ±J Ising models

We start from the so-called uniform classes HCz, SQz, TRz of honeycomb, square and triangular ±J Ising models without exterior magnetic field; z is a fixed number of PAF-bonds on the plaquette perimeter where these bonds have the same positive probability p to be antiferromagnetic and the probability 1−p to be ferromagnetic, the other bonds are always ferromagnetic. For each of these classes we investigate the minimal/maximal ground-state threshold lz,type, uz,type of spontaneous magnetization (type=hc,sq,tr). Based on the notion of PAF-bond node-degree distribution (with respect to a fixed model) we derive special models for which we have strong indications that they just produce the lz,type, uz,type. Estimates for the critical concentrations pc, from simulations with these models, are in good agreement with presumably exact values for the lz,type, uz,type (e.g., in the isotropic cases , , ).