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arXiv:cond-mat/0204032 · physica status solidi (b)

Layering Transitions of the Spin-1/2 Ising Model in a Transverse Magnetic Field

L. Bahmad, A. Benyoussef, Abderrazak Boubekri, Hamid Ez-zahraouy A

Published Oct 1, 1999• 8 citations
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Abstract

Using the mean field theory, the effect of a transverse magnetic field on the layering and wetting transitions of the spin-1/2 Ising model with longitudinal magnetic field is studied. At a fixed value of the temperature smaller than the wetting temperature, such system exhibits a sequence of layering transitions above a critical value of the transverse magnetic field, which depends on the temperature and surface magnetic field.

DOI
10.1002/(sici)1521-3951(199910)215:2<1091::aid-pssb1091>3.0.co;2-d

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Using the mean field theory, the effect of a transverse magnetic field on the layering and wetting transitions of the spin-1/2 Ising model with longitudinal magnetic field is studied. At a fixed value of the temperature smaller than the wetting temperature, such system exhibits a sequence of layering transitions above a critical value of the transverse magnetic field, which depends on the temperature and surface magnetic field.
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability pcp_{c}pc​ above which wetting and layering transitions disappear.
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability pc above which wetting and layering transitions disappear.
The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field theory and Monte Carlo simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely, surface and bulk transition, surface transition, and bulk transition. However, there exist a surface intralayering temperature T(s)(L), above which the surface and the intralayering surface transitions occur. While the bulk layering and intralayering transitions appear above another finite temperature T(b)(L)(>or=T(s)(L)). These surface and bulk intralayering transitions are not seen in the perfect surfaces case. Numerical values of T(s)(L) and T(b)(L), computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. T(s)(L) and T(b)(L) decrease when increasing the system size and/or the surface magnetic field. In particular, T(b)(L) reaches the wetting temperature T(w) for sufficiently large system sizes.
We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension d>2d>2d>2, there is at low strength of randomness and transverse field a phase with true long-range order that is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite-temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e., the logarithm of the diverging time scale rises as a power of the diverging length scale.