Transverse Ising models with spin 1 and mixed spins are studied by use of the discretized path-integral representation and the two-spin cluster approximation. The free energy and the critical transverse field of the systems are obtained.
The transverse-random-field mixed Ising model consisting of arbitrary spin values has been studied by combining the pair model approximation with discretized path-integral representation. The phase diagrams of systems with mixed spins: \ensuremath{\sigma}=1/2, S=1; \ensuremath{\sigma}=1/2, S=3/2, and \ensuremath{\sigma}=1, S=2 are plotted. Not only the discontinuity at T=0 K is found between the trimodal and bimodal distributions of transverse fields, which is similar to the single-spin counterpart, but also the tricritical behavior is observed in these phase diagrams when both transverse fields are trimodal distributed, which is different from the single-spin one. The appearance of tricritical point is independent of the coordination number and spin values. \textcopyright{} 1996 The American Physical Society.
The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.