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

Abstract

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, $1/r^{\alpha }$. 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 $0<\alpha <4$. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near $\alpha \sim 0.5$. We also compute a corse-grained effective Hamiltonian for long wave-length fluctuations. For $0<\alpha <4$ the inverse susceptibility develops a set of continuous minima at wave vectors $|\vec{k}|=k_0(\alpha )$ which dictate the long distance physics of the system. For $\alpha \to 4$, $k_0\to 0$, making the competition between interactions ineffective for greater values of $\alpha$.

8 pages, 3 figures, version accepted for publication in PRE

References in corpus (4)

• Soft Spheres Make More Mesophases
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Orientational order in two dimensions from competing interactions at different scales
• Competing Interactions, the Renormalization Group and the Isotropic-Nematic Phase Transition

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• Domain-wall free energy in Heisenberg ferromagnets
• Stochastic dynamics of planar magnetic moments in a three-dimensional environment
• Nematic order by thermal disorder in a three-dimensional lattice-spin model with dipolar-like interactions
• Emergent Gauge Symmetry in Active Brownian Matter