Universality Aspects of Layering Transitions in Ferromagnetic Blume-Capel Thin Films

TL;DR

This study investigates the critical phenomena and universality in ferromagnetic Blume-Capel thin films, revealing how crystal field interactions influence critical ratios and dimensional crossover, with findings applicable to both spin-1 and spin-1/2 systems.

Contribution

It demonstrates the impact of crystal field interactions on critical ratios and universality classes in ferromagnetic thin films using effective field theory.

Findings

Crystal field interactions affect the critical surface to bulk exchange ratio $R_c$.

Presence of surface exchange enhancement can induce dimensional crossover.

The universality class remains unchanged by crystal field interactions.

Abstract

Critical phenomena and universality behavior of ferromagnetic thin films described by a spin-1 Blume-Capel Hamiltonian has been examined for various thickness values ranging from 3 to 40 layers. Using effective field theory, we have found that crystal field interactions significantly affects the critical value of surface to bulk ratio of exchange interactions $R_{c}$ at which the critical temperature becomes independent of film thickness $L$. Moreover, we have extracted the shift exponent $\lambda$ from computed data. Based on the results, we have shown that in the presence of surface exchange enhancement, the system may exhibit a dimensional crossover. We have also found that presence of crystal field interactions does not affect the value of $\lambda$. Hence, a ferromagnetic spin-1/2 thin film is in the same universality class with its spin-1 counterpart.