Phase Diagrams of the Spin-1 Blume-Capel Film With an Alternating Crystal Field

TL;DR

This paper analyzes the phase diagrams of a spin-1 Blume-Capel film with alternating crystal fields using mean field theory, revealing various topologies, multicritical points, and reentrant behaviors depending on layer parity and crystal field parameters.

Contribution

It provides an analytical study of ground state and finite temperature phase diagrams for alternating crystal fields in spin-1 films, highlighting the effects of layer parity and identifying multicritical phenomena.

Findings

15 types of topology at finite temperature for even layers

14 types of topology at finite temperature for odd layers

Presence of tricritical points and reentrant transition lines

Abstract

The spin-1 ferromagnetic Blume-Capel film with an alternating crystal field $\Delta=\Delta_1$ on the odd layers and $\Delta=\Delta_2$ on the even ones is considered in the mean field approximation. The ground state phase diagrams in the ($d_1,d_2$) plane ($d_1=\Delta_1/J$ and $d_2=\Delta_2/J$) are determined analytically; the number of their phases depends on the parity of the number of layers of the film. At finite temperature, fifteen types of topology, depending on the range of variation of $d_1$, are found in the (t,$d_2$) plane for an even number of layers, but only fourteen for an odd number of layers. The phase diagrams exhibit a variety of multicritical points. In particular, a tricritical point C appears in the paramagnetic-ferromagnetic line of transition, but only for values of $d_1$ larger than a threshold value $d_{trc}^{(2)} ={8 \ln 2 \over 3}$ which is but the tricritical crystal field (in the mean field approximation) of the spin-1 Blume-Capel model on a square lattice. Moreover, lines of transition presenting the reentrant and double reentrant behaviors may also take place.