Equilibrium Properties of the Spin-1 Ising System With Bilinear, Biquadratic and Odd Interactions

Abstract

The equilibrium properties of the spin-1 Ising system [1] Hamiltonian with arbitrary bilinear (J), biquadratic (K) and odd (L), which is also called dipolar-quadrupolar [2], interactions are studied for zero magnetic field by the lowest approximation of the cluster variation method [3]. The odd interaction is combined with the bilinear and biquadratic exchange interactions by the geometric mean. In this system, phase transition depends on the ratio of the coupling parameter, $\\alpha$ = J/K, therefore, changing of the phase transitions with a is investigated extensively and found that for $\\alpha\\leq 1$ and $\\alpha\\geq 2000$ a second-order phase transition occur, and for $1 < \\alpha < 2000$ a first-order phase transition occur. The critical temperatures in the case of the second-order phase transition and the upper and lower limit of stability temperatures in the case of the first-order phase transition are obtained for different values of a calculating by the Hessian determinant. The first-order phase transition temperatures are found by using the free energy values while increasing and decreasing the temperature. The unstable solutions for the first-order phase transitions are obtained by displaying the free energy surfaces in the form of the contour mapping. Results are compared with the spin-1 Ising system Hamiltonian with only bilinear and biquadratic interactions [4] and found that the odd interaction influences the phase transitions very much.