Effective field approach to the Ising film in a transverse field

TL;DR

This paper investigates the phase transition behavior of a spin-1/2 Ising film in a transverse field using effective field theory, analyzing how surface interactions and film thickness influence critical temperatures.

Contribution

It introduces a detailed analysis of the critical temperature dependence on surface exchange interactions and film thickness within the effective field framework.

Findings

Critical temperature varies with surface interaction ratio R.

For R < Rc, Tc approaches bulk critical temperature as R increases.

For R > Rc, Tc exceeds bulk and surface critical temperatures, approaching surface temperature.

Abstract

We study the phase transitions of the spin-1/2 Ising film in a transverse field within the framework of the effective field theory. We evaluate 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 Tc^B/J and approaches Tc^B/J as R increases further. On the other hand, if R>Rc, Tc/J is larger than both the bulk Tc^B/J and the surface Tc^S/J critical temperatures of the corresponding semi-infinite system, and approaches Tc^S as R increases further.