An effective field theory study of layering transitions in Blume–Capel thin films in the presence of quenched random crystal fields

In the presence of quenched random crystal fields, phase transitions in magnetic thin films described by the spin-1 Blume–Capel model have been investigated using effective field theory (EFT). Crystal field disorder has been sampled by introducing dilute and trimodal random crystal fields. For dilute crystal fields, in the highly anisotropic limit ( D → ∞ ) , we have found that the critical value of the surface to bulk ratio of exchange interactions ( R c ) at which the second-order transition temperature becomes independent of the film thickness is a spin-dependent property of thin magnetic films. Moreover, as a percolation problem, we have performed detailed calculations in the limit D → − ∞ , and it has been shown that a novel feature emerges in the presence of enhanced surfaces. Besides, for trimodal random crystal fields, the variation of the special point R c as a function of the random field parameters has been elucidated. Finally, in the limit D → ∞ , based on the numerical data provided by EFT, we have introduced an analytical expression for the variation of R c as a function of the randomness parameter p of the trimodal distribution.