Effects of the randomly distributed magnetic field on the phase diagrams of the transverse Ising thin film

The effect of the zero centered Gaussian random magnetic field distribution on the phase diagrams and ground state magnetizations of the transverse Ising thin film has been investigated. As a formulation, the differential operator technique and decoupling approximation within the effective field theory has been used. The variation of the phase diagrams with the Gaussian distribution width (\sigma) has been obtained and particular attention has been paid on the evolution of the special point coordinate with distribution parameter. In addition, the ground state longitudinal and transverse magnetization behaviors have been investigated in detail.