Critical Properties of a Spin-1/2 Ising Bilayer System in a Transverse Field

Abstract

Within the framework of the effective-field theory, the phase diagram (transition temperature T c and critical transverse field W c ) of a ferroelectric bilayer system is studied on the basis of the spin-1/2 transverse Ising model consisting of two different ferroelectric slabs with the same thickness L. The dependences of T c and W c on L and the inter-slab exchange coupling R are examined and discussed. We find some unexpected phenomena in the phase diagrams of the system with a thin thickness L, such as the frustration effect due to the large values of R and transverse field W.

Phase Diagrams of a Transverse Ising Multilayer System with a Higher Spin Value

“…In Section 4, furthermore, the temerature dependences of the longitudinal magnetization are studied numerically for the multilayer systems with spin-1/2 and spin-1 ferroelectric slabs stacked antiferroelectrically. We have also found many characteristic phenomena similar to those in [14].…”

“…The coefficients A n and B n (n = 1 to 2) in (13) and (14) are defined by respectively, where these coefficients can be easily calculated by the use of a mathematical formula exp (ar) f(x) = f(x + a).…”

“…The behavior of the critical transverse field W c at which the T c versus W curve reduces to zero was also studied in [13] within the frameworks of MFA and EFT. Very recently, Kaneyoshi and Shin [14] have investigated the T c and W c dependences of R and L in spin-1/2 transverse Ising bilayer and multilayer systems, using the EFT. Then, a number of unexpected phenomena, such as the reduction of T c and W c to zero, has been found in the phase diagrams when large values of R and W are selected.…”

“…1/2) ferroelectric slabs, especially paying attention to the effect of spin value S on the phase diagrams. In Section 2, a formulation is given for the systems with L = 1 and 2, since many characteristic features of the multilayer system with arbitrary L can be observed in them [14]. In Section 3, the numerical results of the phase diagrams are examined in detail.…”

“…the multilayer system with L = 1 are shown by selecting two values of W and S; W/J = 0.5 and S = 1/2 for curve A, W/J = 2.0 and S = 1/2 for curve B, W/J = 0.5 and S = 1 for curve A H , and W/J = 2.0 and S = 1 for curve B H .Here, the curves A and B are equivalent to those obtained in[14] for the spin-1/2 transverse Ising multilayer system with L = 1. The T c curve labeled B starts to take a finite value at a critical value of R near R = 1.0.…”