Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N = 4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T, alpha) space (alpha = J(2)/J(1)), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2 < alpha < 0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for 01 = 1.0. Our results for alpha = 1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition. (C) 2007 Elsevier B.V. All rights reserved.