Blume-Emery-Griffiths model on the honeycomb lattice

Abstract

Exact results are obtained for a spin-1 system on the honeycomb lattice with the Blume-Emery-Griffiths Hamiltonian −ℋ/kT =J∑ _i,j S _i S _j +K∑〈i,j〉S ² _i ² _j −Δ∑ _i S ² _i +H∑S _i subject to the constraintK=−ln coshJ. ForJ>0, the system behaves like a spin-1/2 Ising ferromagnet with the free energy analytic everywhere except at the first-order phase boundaryH=0, tanhJ<(2+e ^Δ)/$\sqrt 3$. Derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization. ForJ<0, the system can be transcribed into an antiferromagnetic spin-1/2 Ising model in a real magnetic field, and from this equivalence portions of the exact phase boundary are determined.