We study dimerized spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies by means of Jordan-Wigner transformation. The system has a hidden conserved quantity with which it can be exactly mapped onto spin-1/2 transverse Ising model. We obtained analytical expressions of quasi-particles' spectra, minimal energy gap for exciting a fermion quasi-particle, minimal energy gap for exciting a hole, transverse magnetism, static transverse susceptibility, the nearest neighboring longitude spin-spin-correlation function and ground state phase diagram. It shows that ground states of system are strongly dependent on system parameters. As system parameters periodly change, a series of quantum phase transition appear.

The real-space renormalization group approach is used for quasi-periodic layered ferromagnetic super lattice in which a site with spin s_a or s_b,between layers the exchange energy are J₁ and J₂, which are arranged in quasi-periodic Fibonacci sequence, and exchange energy J₀ in each layer. When J₁=J₂=J₀, we obtained an exact decimation transformation for local magnons of layers α,β(γ) and б(τ)in the ferromagnets. Iteration of the transformation provides numerical results for the local density of states (LDOS) and the magnetization. We found the band widthes of LDOS of layers depend on J₁, J₂, s_a adn s_b.