Effect on the groundstate threshold p(c) by different boundary conditions in 2D +/- J Ising models

In the so-called uniform classes HCz, SQ(z), TRz of random honeycomb, squar e and triangular +/- J Ising models without exterior magnetic field, we inv estigate the effect of periodic and mixed lattice boundary conditions (b.c. ) on the groundstate threshold p(c) of the spontaneous absolute magnetizati on per spin; z is a fixed number of PAF-bonds on the plaquette perimeter wh ere these bonds have the same positive probability p to be antiferromagneti c and the probability 1 - p to be ferromagnetic, the remaining bonds are fe rromagnetic. For the models in the uniform classes it turns out that period ic b.c. ensure the existence of a critical concentration p(c,p.b.c) (at zer o temperature). Whereas for mixed b.c. (periodic b.c. in one direction, and in the orthogonal direction only couplings +1 on opposite boundaries) ther e are, in the classes SQ(1) and TR1, models for which p(c,m.b.c). does not exist. The emphasis is on models in classes SQ(1), TR1, HC1, as a counterpa rt to isotropic models. For z = 1, by means of simulations of exact grounds tates, we have strong support that there is a first-order phase transition in the magnetization, in several models. For p(c) in the three regular isot ropic models we give a simple formula based on the lattice node degree. (C) 2000 Elsevier Science B.V. All rights reserved.