24,299 research outputs found
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
Approximate solution for Fokker-Planck equation
In this paper, an approximate solution to a specific class of the
Fokker-Planck equation is proposed. The solution is based on the relationship
between the Schr\"{o}dinger type equation with a partially confining and
symmetrical potential. To estimate the accuracy of the solution, a function
error obtained from the original Fokker-Planck equation is suggested. Two
examples, a truncated harmonic potential and non-harmonic polynomial, are
analyzed using the proposed method. For the truncated harmonic potential, the
system behavior as a function of temperature is also discussed.Comment: 12 pages, 8 figure
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