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

• Published in: Physics letters. A 2008-02, Vol.372 (8), p.1180-1184
• Main Authors: dos Anjos, Rosana A., Roberto Viana, J., Ricardo de Sousa, J.
• Format: Article
• Language: English
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2007.09.059

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 , α ) space ( α = 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 < α < 0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α = 1.0 . Our results for α = 1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.