  We use improved Monte-Carlo algorithms to study the antiferromagnetic
2D-Ising model with competing interactions $J_1$ on nearest neighbour and $J_2$
on next-nearest neighbour bonds. The finite-temperature phase diagram is
divided by a critical point at $J_2 = J_1/2$ where the groundstate is highly
degenerate. To analyse the phase boundaries we look at the specific heat and
the energy distribution for various ratios of $J_2/J_1$. We find a first order
transition for small $J_2 > J_1/2$ and the transition temperature suppressed to
$T_C=0$ at the critical point.
