Ground-state morphology of random frustrated XY systems

Analytical and numerical results are presented on the ground-state properties of the frustrated XY spin model. One isolated antiferromagnetic (AF) bond in a periodic lattice of ferromagnetic bonds of strength J gives rise to a canted Villain ground state only if its strength exceeds a critical value Kc (Kc=J for the square lattice). When two AF bonds are present, their interaction is short range below the threshold and long range (power law) above, and we give a Ginzburg-Landau energy functional that incorporates analytical results for that situation. For a finite density of randomly distributed AF bonds, numerical simulations on the square lattice show that the nature of the ground states differs markedly for small and large values of K/J, and a simple coherent-potential-approximation calculation is presented for the location of the line separating the two regimes. The simulations also indicate the existence of locally ordered domains, limited by grain boundaries pinned to strongly frustrated regions. A similar model has recently been invoked to interpret spin-glass-type features observed on microscopic scales in cuprate compounds for compositions close to the high-Tc superconductors, and the relevance of the results for these materials is briefly discussed.