Ground-state phase diagram of the mixed spin-1/2 and spin-1 Ising chain with axial and rhombic zero-field splitting parameters is exactly calculated within the framework of the transfer-matrix method. It is shown that the rhombic zero-field splitting parameter prefers the magnetically ordered phase instead of the disordered phase.
The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension γ_{λ} and fixed-points' structure. The dynamic exponent z is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed.
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