We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an antiferromagnetic (AF) coupling J[over ]>0, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a Néel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.

We calculate the magnetic and quasiparticle excitation spectra of an itinerant J(1)-J(2) model for iron-pnictide superconductors. In addition to an acoustic spin-wave branch, the magnetic spectrum has a second, optical branch, resulting from the coupled four-sublattice magnetic structure. The spin-wave velocity has also a planar directional anisotropy, due to the collinear or striped antiferromagnetism. Within the magnetically ordered phase, the quasiparticle spectrum is composed of two Dirac cones, resulting from the folding of the magnetic Brillouin zone. We discuss the relevance of our findings to the understanding of both neutron scattering and photoemission spectroscopy results for SrFe(2)As(2).

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The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.