Groundstate threshold in triangular anisotropic +/− J Ising models

Abstract

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 p c, 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 < p c, tr ( q, 0) for t|0.25 − q t|⩾0.125 and to 0.5 − q p c, tr ( q, 0) for t|0.25 − q t| < 0,125, with the suggestion p c, tr (0.25, 0) = 0.25. Analytically we got p c, tr (0, 0) ⩽1, ensuring a phase transition in TR(p, 0, 0) at all. The surface p c, tr ( q, r) is compared to p c, hc ( q, r) which is associated with honeycomb lattices HC(p, q, r). We give presumably exact critical concentrations p c at groundstates for basic lattices in 19 subclasses from so-called uniform classes of triangular, square and honeycomb +/− J Ising models.