The frustrated bilayer Ising model: A cluster mean-field approach

We investigate the Ising model on the bilayer square lattice with antiferromagnetic interactions between first-(J1) and second-neighbors (J2) inside each layer and a perpendicular antiferromagnetic interaction (Jp) between layers. The roles of frustration and interlayer interactions on the thermal phase transitions are described within a variational cluster mean-field (CMF) approach. For J2/J1<1/2, the model exhibits a Néel antiferromagnetic (AF) ground state and, for J2/J1>1/2, a stripe antiferromagnetic (SAF) ground state takes place. In the absence of interlayer interactions, a tricritical point is found in the phase boundary between SAF and paramagnetic (PM) phases. Our CMF calculations show that the ordering temperature of both AF and SAF phases is enhanced by the interlayer couplings. We also show that, at different levels of frustration, in the strong-interlayer-coupling limit, the ordering temperature is twice the one in the absence of interlayer interactions. At the weak-interlayer-coupling limit, a linear dependence of the ordering temperature with the interlayer interaction is observed, which indicates a shift exponent ϕ=1. Our investigation revealed that the model exhibits tricriticality at all strengths of the interlayer interactions, but the coupling coordinate of the tricritical point (J2/J1)t exhibits a minimum at a finite strength of Jp/J1. However, in the strong interlayer coupling limit, the coupling coordinate of the tricritical point is the same as in the decoupled (Jp=0) limit. Therefore, our CMF study reveals a persistent tricriticality in the frustrated bilayer Ising model.