The transverse spin-1 Ising model with a longitudinal crystal field presents a rich variety of critical phenomena. Using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions, the phase diagrams and the tricritical points are investigated for the square lattice (N=4). The results show that the tricritical points exist for certain values of the strength of the transverse field and the strength of the longitudinal crystal field. The longitudinal and the transverse magnetizations as well as the longitudinal and the transverse quadrupolar moments are also examined. These quantities as functions of the temperature, the strength of the longitudinal crystal field and the strength of the applied transverse field are calculated numerically and some interesting results are obtained.

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections.

Within the framework of the effective field theory, based on the use of a probability distribution technique that correctly accounts for the single site kinematic relations, we examine the phase transitions of a magnetic transverse Ising superlattice consisting of two ferromagnet Ising materials with spins mu = 1/2 and S = 1, respectively, on a simple cubic structure. The critical temperature of the system is studied as a function of the interface coupling, the thickness of the constituents in a unit cell. A critical value of the interface exchange interaction above which the interface magnetism appears is found. The effects of the transverse field on the critical behavior of the system are also investigated.

The temperature dependences of the layer parameters σn,z= , mn,z= and qn,z= of a magnetic Ising superlattice consisting of two ferromagnetic Ising materials with spins μ=1/2 and S=1 respectively, on a simple cubic structure, are examined using the effective field theory based on the use of a probability distribution technique that correctly accounts for the single site kinematic relations. According to the values of the exchange interactions, different qualitative types of phase diagrams are expected.