GROUND-STATE PROPERTIES OF FINITE SQUARE AND TRIANGULAR ISING LATTICES WITH MIXED EXCHANGE INTERACTIONS

Small Ising lattices with both ferromagnetic (F) and antiferromagnetic (AF) exchange interactions (or bonds) and increasing numbers of spins are studied by means of two independent methods: computational soluti ons to the Hamiltonian problem and topological counting of frustration paths. Equal magnitudes and concentrations are assumed for both types of bonds. Two different geometries are considered: square lattices (S L's) with coordination number 4 and triangular lattices (TL's) with co ordination number 6. Two-dimensional samples with a total number of sp ins N between 4 and 64 are considered for SL's, while N is varied betw een 4 and 44 for TL's. They are distributed in two-dimensional arrays where periodic boundary conditions are imposed. After an array is sele cted, bond distributions (samples) are independently and randomly gene rated in fixed positions. The physical parameters are then calculated exactly for each sample. The emphasis here is on the ground-state prop erties and their dependence with size and shape for the two kinds of l attices. All magnitudes correspond to a basic statistics over a large number of samples for each array. The following magnitudes are reporte d: ground-state energy per bond, frustration segment, abundance of fir st excited states, remnant entropy, low-temperature specific heat, and site order parameters q, p, and h. Parameters p and h are introduced here, showing advantages over other similar magnitudes. The results ar e in good correspondence with analytic studies for the thermodynamic l imit. This means that the spin site correlation (p) tends to vanish as N grows. However, we have found that the shape dependence modulates t he behavior of these systems toward the thermodynamic limit. There is no tendency to vanish for the bond correlation parameter (h). For both kinds of lattices h might be a constant independent of size and shape .