The Phase Transition of the Spin‐1/2 Ising Model with a Random Field

Henrique E. Borges, P. R. Silva

V. K. Saxena

Recently, there has been interest in the problems of disorder in the Ising model in a transverse field, which may apply to DKDP-KDP mixed systems and diluted vanadates. The site and bond diluted transverse Ising models have already been studied using Green's function techniques along with the coherent potential approximation. However, the situation as regards to the existence of a second order phase transition and the divergence of the static susceptibility is not very clear. In the present paper, a spin ½ Ising model in a transverse field and random bond (site) dilution is studied by variational cluster and perturbation expansion method. The critical temperature for the existence of a second order phase transition is calculated as a function of concentration of bonds (spins) and the transverse field. Variation of the critical concentration, for the existence of phase transition, is studied as a function of the transverse field. A phase diagram in the temperature-concentration-transverse field space is constructed. The static susceptibility is calculated and is found to diverge at the critical temperature, as is expected for the existence of a second order phase transition.

Fumihiko Takano

Yu‐qiang Ma, Chang-De Gong

Random field spin- S Ising model with a transverse field has been studied by making use of the pair approximation with the discretized path-integral representation, and an analytical expression of second-order phase transition is derived for all the symmetric probability distributions of (longitudinal) random fields. The phase diagrams at T = 0 are obtained, and the conditions for existence of tricritical points are examined for an arbitrary number of nearest-neighbor spins.

Yu‐qiang Ma, Y. G., C. D. Gong

Abstract The quantum spin‐1 Ising system with random fields is investigated by combining the pair approximation with the discretized path‐integral representation. An analytical expression for the second‐order phase transition is derived for all symmetrical probability distributions of random fields, and phase diagrams for Gaussian and bimodal random fields are obtained numerically.

Fa Yueh Wu