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physica status solidi (b)

Phase Diagrams of the Semi-Infinite Spin-1/2 Ising Model and Spin-1/2 Ising Film in a Random Transverse Surface Field

B. Laaboudi, M. Saber, M. Kerouad

Published Mar 1, 1999• 7 citations
Publisher

Abstract

The critical behavior of both semi-infinite spin-1/2 Ising system and spin-1/2 Ising film in a random transverse surface field has been studied within an effective field theory. The effect of the ratio R of the surface exchange interaction to the bulk one, random transverse surface field and film thickness on the phase diagrams are investigated.

DOI
10.1002/(sici)1521-3951(199903)212:1<153::aid-pssb153>3.0.co;2-4

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Acta Physica Sinica•Jan 1, 1997•1 citation
The critical behavior of both semi-infinite spin-1/2 Ising system and spin-1/2 Ising film in a random transverse surface field has been studied within an effective field theory. The effect of the ratio R of the surface exchange interaction to the bulk one, random transverse surface field and film thickness on the phase diagrams are investigated.
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.
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.
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.