Effect on the groundstate threshold pc by different boundary conditions in 2D ±J Ising models

In the so-called uniform classes HCz, SQz, TRz of random honeycomb, square and triangular ±J Ising models without exterior magnetic field, we investigate the effect of periodic and mixed lattice boundary conditions (b.c.) on the groundstate threshold pc of the spontaneous absolute magnetization per spin; 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 remaining bonds are ferromagnetic. For the models in the uniform classes it turns out that periodic b.c. ensure the existence of a critical concentration pc,p.b.c. (at zero temperature). Whereas for mixed b.c. (periodic b.c. in one direction, and in the orthogonal direction only couplings +1 on opposite boundaries) there are, in the classes SQ1 and TR1, models for which pc,m.b.c. does not exist. The emphasis is on models in classes SQ1, TR1, HC1, as a counterpart to isotropic models. For z=1, by means of simulations of exact groundstates, we have strong support that there is a first-order phase transition in the magnetization, in several models. For pc in the three regular isotropic models we give a simple formula based on the lattice node degree.