Weak ferromagnetism and spiral spin structures in honeycomb Hubbard planes

Within the Hartree Fock- RPA analysis, we derive the spin wave spectrum for the weak ferromagnetic phase of the Hubbard model on the honeycomb lattice. Assuming a uniform magnetization, the polar (optical) and acoustic branches of the spin wave excitations are determined. The bipartite lattice geometry produces a q-dependent phase difference between the spin wave amplitudes on the two sub-lattices. We also find an instability of the uniform weakly magnetized configuration to a weak antiferromagnetic spiraling spin structure, in the lattice plane, with wave vector Q along the Gamma-K direction, for electron densities n>0.6. We discuss the effect of diagonal disorder on both the creation of electron bound states, enhancement of the density of states, and the possible relevance of these effects to disorder induced ferromagnetism, as observed in proton irradiated graphite.Comment: 13 pages, 7 figure

Percolation study for the capillary ascent of a liquid through a granular soil

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {\lambda} of the capillary bridges among grains. Low {\lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {\lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {\lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {\lambda}_{c} = (0.049 \pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {\nu} = (0.830 \pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of $D$.Comment: 11 pages, 2 ps figures include