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/r(α). 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[over arrow]|=k(0)(α) which dictate the long-distance physics of the system. For α→4, k(0)→0, making the competition between interactions ineffective for greater values of α.