CONTINUOUS- AND FIRST-ORDER PHASE TRANSITIONS IN ISING ANTIFERROMAGNETS WITH NEXT-NEAREST- NEIGHBOUR INTERACTIONS

Both the square and triangular (sing antiferromagnetic systems with next-nearest neighbour interactions are studied by a new efficient entropic scheme. Using the energy distribution and order parameter's fourth order cumulant it is illustrated that the two models behave quite differently. For the square model we establish strong numerical evidence showing a continuous - transition scaling, whereas for the triangular model a first-order transition is verified. Our results - are compared with the existing predictions and controversies in the literature.