Monte Carlo studies of the Ising square lattice with competing interactions

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 $J_2=J_1\mathrm{/}2$ 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 $J_2\mathrm{/}{J}_1$. We find a first order transition for small $J_2>J_1\mathrm{/}2$ and the transition temperature suppressed to $T_C=0$ at the critical point.