Nematic phase in two-dimensional frustrated systems with power-law decaying interactions

We address the problem of orientational order in frustrated interaction systems as a function of the relative range of the competing interactions. We study a spin model Hamiltonian with short-range ferromagnetic interaction competing with an antiferromagnetic component that decays as a power law of the distance between spins, 1/rα. These systems may develop a nematic phase between the isotropic disordered and stripe phases.We evaluate the nematic order parameter using a self-consistent mean-field calculation. Our main result indicates that the nematic phase exists, at mean-field level, provided 0 < α < 4. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near α ∼ 0.5.We also compute a coarse-grained effective Hamiltonian for long wavelength fluctuations. For 0 < α < 4 the inverse susceptibility develops a set of continuous minima at wave vectors | k| = k0(α) which dictate the long-distance physics of the system. For α → 4, k0 → 0, making the competition between interactions ineffective for greater values of α