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We reexamine the tunneling density of states in quantum dots and nanoparticles within the model which is extension of the universal Hamiltonian to the case of uniaxial anisotropic exchange. We derive the exact analytical result for the tunneling density of states in the case of arbitrary single-particle energy spectrum. We find that, similar to the case of the isotropic exchange, the tunneling density of states as a function of energy has the maximum due to a finite value of the total spin of the ground state near the Stoner instability. We demonstrate that there are no additional extrema which have been predicted on the basis of perturbative analysis [M.N. Kiselev and Y. Gefen, Phys. Rev. Lett. {\bf 96}, 066805 (2006)]., Comment: 11 LaTex pages, 3 figures

We explore the static longitudinal and dynamic transverse spin susceptibilities in quantum dots and nanoparticles within the framework of the Hamiltonian that extends the universal Hamiltonian to the case of uniaxial anisotropic exchange. For the limiting cases of Ising and Heisenberg exchange interactions we ascertain how fluctuations of single-particle levels affect the Stoner instability in quantum dots. We reduce the problem to the statistics of extrema of a certain Gaussian process. We prove that, in spite possible strong randomness of the single-particle levels, the spin susceptibility and all its moments diverge simultaneously at the point which is determined by the standard criterion of the Stoner instability involving the mean level spacing only., Comment: 23 pages, 8 figures

We explore the effect of single-particle level fluctuations on the Stoner instability in a QD with a strong spin-orbit coupling in the framework of the universal Hamiltonian with the Ising exchange interaction. We reduce the problem to studying the statistics of extrema of a certain Gaussian process and demonstrate that, in spite of the randomness of the single-particle levels, the longitudinal spin susceptibility and all its moments diverge simultaneously at the point of the Stoner instability which is determined by the standard criterion involving the mean level spacing only., Comment: LaTeX 5+5 pages, 1 figure

The co-tunneling current through a two-level doubly occupied quantum dot weakly coupled to ferromagnetic leads is calculated in the Coulomb blockade regime. It is shown that the dependence of the differrential conductance on applied voltage has a stair-case structure with different sets of "stairs" for parallel and anti-parallel configurations of magnetization of the leads. Contributions to the current from elastic and inelastic processes are considered distinctly. It is observed that the interference part of the co-tunneling current involves terms corresponding to inelastic processes. Dependence of the co-tunneling current on the phases of the tunneling amplitudes is studied., Comment: LaTex, 14 pages