Abstract The phase diagram of a transverse Ising thin film is investigated by the use of two theoretical frameworks, namely the standard mean field theory and the effective field theory. The effects of the ratio p between the bulk and surface transverse fields on the critical temperature are discussed by including the modification of surface exchange interaction. Some characteristic features are found in the phase diagrams when the ratio p increases from p = 1.0. They are enhanced for the film with thickness L smaller than 5.0. In particular, the critical ratio at which the critical temperature of the film with a finite transverse field reduces to zero, being independent of L, exhibits a linear relation when it is plotted against the modification of surface exchange interaction.
Within the framework of the effective field theory, we examine the phase transitions of the spin-12 Ising film in a transverse field. We study the critical temperature of the film as a function of the exchange interactions, the transverse field and the film thickness. We find that, if the ratio of the surface exchange interactions to the bulk ones R=Js/J is smaller than a critical value Rc, the critical temperature Tc/J of the film is smaller than the bulk critical temperature TcB/J and as R is increased further, Tc/J approaches TcB/J. On the other hand, if R>Rc, Tc/J is larger than the bulk TcB/J and the surface TcS/J critical temperatures of the corresponding semi-infinite system and as R is increased further, Tc/J approaches the surface critical temperature Tcs/J.
Within the framework of the effective-field theory, we examine the phase transitions of a transverse spin-
21 Ising film. The critical temperatures of the film as a function of the interactions, transverse fields, and film thickness are studied. It is found that for the ratio of the surface interactions to the bulk ones
R=Js/J less than a critical value
Rc, the critical temperature
Tc/J of the film is smaller than the bulk critical temperature
TcB/J and as the film thickness L is increased further,
Tc/J increases and approaches asymptotically
TcB/J for large values of L. However, for
R>Rc,Tc/J is larger both than the bulk
TcB/J and the surface
TcS/J critical temperatures of the corresponding semi-infinite system and as the film thickness L is increased further,
Tc/J decreases and approaches asymptotically, for large values of L, the surface magnetic transition
TcS/J observed in the corresponding semi-infinite system. We calculate also some magnetic properties of the film such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility, but its magnitude is reduced. Also there is a rounded peak at the bulk critical temperature when
R>Rc. The bulk related character of the susceptibility is more pronounced and the surface related character is less pronounced when the film thickness is large.
An effective-field theory that accounts for the self-spin correlation function is used to study the effect of surface dilution on the critical behavior of a ferromagnetic Ising film in transverse surface and bulk fields. Surface exchange enhancement (or reduction) is considered. It is shown that the surface and bulk fields affect the critical ratio of surface to bulk interactions, at which the surface orders before the bulk, in opposite ways. Although it is found that for the undiluted film this leads to a critical ratio that is practically insensitive to field for common bulk and surface field strengths, this feature is relaxed to a certain degree with surface dilution. The thickness dependence of the critical temperature, and phase diagrams in the fields, interaction strength ratio, and dilution parameter space, are presented.
Abstract The phase diagram of the three‐dimensional transverse Ising system with competing surface and bulk exchange interactions is studied by the use of an effective‐field method within the framework of a single‐site cluster theory. In addition to this pure case, which shows qualitatively interesting features, we investigated the effects of the bond dilution on the obtained phase diagram. In particular, we studied the influence of the surface dilution parameter on the surface transitions. We find a number of characteristic behaviours of the surface both in the absence and in the presence of the surface transverse field. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)