Nematic phase without Heisenberg physics in FeAs planes

We use Monte Carlo simulations and analytical arguments to analyze a frustrated Ising model with nearest-neighbor antiferromagnetic coupling J(1) and next-nearest-neighbor coupling J(2). The model is inspired on the physics of pnictide superconductors and to some extent we argue that it can be more representative of this physics than the Heisenberg counterpart. Parameters are chosen such that the ground state is a columnar or striped state, as observed experimentally, but is close to the transition to the simple Neel ordered antiferromagnetic state R = J(2)/vertical bar J(1 vertical bar) greater than or similar to 0.5. We find that a nematic phase is induced close to R = 0.5 by finite-size effects and argue that this explains experiments in imperfect samples that find a more robust nematic state as the quality of the sample decreases [A. Jesche et al., Phys. Rev. B 81, 134525 ( 2010)]. Including the effect of a weak coupling with the lattice, we find that a structural transition occurs associated with a nematic phase, with a magnetic transition occurring at a lower temperature. These two transitions merge into a single structural and magnetic transition with a stronger first-order character for larger spin-lattice couplings. These two situations are in agreement with the different phenomenologies found in different families of pnictides.