Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J1 on nearest neighbour and J2 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 critical point at J2 = 0.5J1. Further on we investigate the character of the different phase boundaries and find that the transition is weakly first order for moderate J2 > 0.5J1. PACS. 05.50.+q Lattice theory and statistics including Ising, Potts models, etc – 75.10.Hk Classical spin models – 64.60.De Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc)