There are two ground states for T/Jnn > 0:
For the AFI-state we find a second-order transition into disorder. Critical exponents are of the 3d-nn-Ising class and appear not to change from a = 0 to 0.245. The AFII-disorder phase boundary is determined to be first order, as well as the AFI-AFII transition. The three critical lines meet at an umbilical point close to T/Jnn = 1.15 and a = 0.25. The exact location and nature of that critical point could not be determined due to a combination of low temperature, critical slowing down, and high degeneracy of the ground state. We assume that strong crossover effects complicate finite-size analysis in the vicinity of this critical point. Extensive simulations hint towards the point being located at a value of a slightly greater than 0.25.
Ralf K. Heilmann,
Alan M. Ferrenberg,
David P. Landau, and Rainer W. Gerling,
" Histogram Monte Carlo Study of Phase Transitions in a Highly Degenerate System",
in Computer Simulation Studies in Condensed Matter Physics IV,
D. P. Landau, K. K. Mon, H.-B. Schüttler (Eds.), Springer Proceedings in Physics 72, Springer Verlag Berlin (1993)