Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J(1) on nearest neighbour and J(2) on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the criticalpoint at J(2) = J(1)/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J(2) > J(1)/2.