Critical properties of a spin- Ising model with bilinear and biquadratic interactions

We have studied the temperature dependences of the magnetization and the quadrupolar moment of a spin- Ising model Hamiltonian with bilinear and biquadratic interactions using the molecular field approximation. A number of characteristic behaviors for the thermal variations of the order parameters are investigated and besides the stable solutions, metastable and unstable solutions are found. These solutions are classified by the means of free energy surfaces based on the form of a contour map. The first- and second-order phase transition temperatures are found by using free energy values while increasing and decreasing the temperature, and the Hessian determinant, respectively. The metastable phase diagram in addition to the equilibrium phase diagram is presented in (T/K,J/K) plane in detail and it exhibits zero-temperature critical point, critical points, triple point, tricritical points and multicritical point.