Groundstate threshold in triangular anisotropic +/−J Ising models

We deal with anisotropic triangular +/− J Ising spin lattices TR(p, q, r) with antiferromagnetic coupling probabilities p, q, r (p for the horizontal bonds and q, r for the other two directions, respectively). Non-antiferromagnetic bonds are ferromagnetic. The groundstate phase transition surface pc,tr(q, r) is investigated, concerning its border (here a phase transition reflects the disappearance of spontaneous magnetisation). To this end, for reasons of symmetry it suffices to study TR(p, q, r). Results from simulations lead to 0.5 − q < pc, tr(q, 0) for t0.25 − q t 0.125 and to 0.5 − q pc, tr(q, 0) for t0.25 − q t < 0,125, with the suggestion pc, tr(0.25, 0) = 0.25. Analytically we got pc, tr(0, 0) 1, ensuring a phase transition in TR(p, 0, 0) at all. The surface pc, tr(q, r) is compared to pc, hc(q, r) which is associated with honeycomb lattices HC(p, q, r). We give presumably exact critical concentrations pc at groundstates for basic lattices in 19 subclasses from so-called uniform classes of triangular, square and honeycomb +/−J Ising models