E ective eld approach to the Ising lm in a transverse eld

Within the framework of the e ective eld theory, we examine the phase transitions of the spin1 2 Ising lm in a transverse eld. We study the critical temperature of the lm as a function of the exchange interactions, the transverse eld and the lm thickness. We nd 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 lm is smaller than the bulk critical temperature T B c =J and as R is increased further, Tc=J approaches T B c =J . On the other hand, if R¿Rc, Tc=J is larger than the bulk T B c =J and the surface T S c =J critical temperatures of the corresponding semi-in nite system and as R is increased further, Tc=J approaches the surface critical temperature T s c =J . c © 1999 Published by Elsevier Science B.V. All rights reserved.