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.
Within the framework of the effective field theory, with a probability distribution technique that accounts for the single-site spin correlations, we examine the critical behavior of a diluted spin-1/2 Ising film. The critical temperature of the system is studied as a function of the thickness of the film, the concentration of magnetic atoms, the strength of the transverse field and the couplings. It is shown that for the ratio of the surface couplings to the bulk ones R = Js/J less than a critical value R,, the critical temperature of the film Tc/J is smaller than the bulk critical temperature Tc^B/J and for R ≥ Rc, Tc/J is larger than the bulk critical temperature Tc^B/J and Tc^S/J of the corresponding semi-infinite system. As the film thickness L is increased further Tc/J increases for R ≤ Rc (decreases for R 2 R,) and approaches asymptotically for large values of L the bulk critical temperature Tc^B/J (the surface critical temperature Tc^S/J) of the corresponding semi-infinite system.
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.
Abstract By the use of both the standard mean field theory and the effective field theory with correlations the phase transition of the transverse Ising thin films is investigated with special emphasis to the behavior of the susceptibility χ(T) outside the critical regime. The exchange interaction and transverse field at the surfaces of the thin film take values different from those in the bulk. Various non‐monotonic temperature dependences of the effective exponent γ(T) introduced by Kouvel and Fisher are found, depending on the ratios of these properties between the surfaces and the bulk as well as the value of film thickness L. They are clearly different from the behavior in the bulk. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)