Pseudospin Approach to Linear Antiferromagnetic Chains

The generalized linear antiferromagnetic chain with two spins per unit cell $J>0$, and $a, b, d, e>~0$, ${H}G={Σ}{N/2}{j=1}J{a{{S}₂ⱼ}ᶻ{{S}₂ⱼ₊₁}ᶻ+b({{S}₂ⱼ}ˣ{{S}₂ⱼ₊₁}ˣ+{{S}₂ⱼ}ʸ{{S}₂ⱼ₊₁}ʸ)+d{{S}₂ⱼ}ᶻ{{S}_{2j{-}1}}ᶻ+e({{S}₂ⱼ}ˣ{{S}_{2j{-}1}}ˣ+{{S}₂ⱼ}ʸ{{S}_{2j{-}1}}ʸ)},$ is solved in the pseudospin approximation. The pseudospin method is compared with the exactly soluble special case of the Heisenberg-Ising antiferromagnet ($a=b=1+{δ}$, $d=1{-}{δ}$, $e=0$) and good agreement is obtained even for a sensitive property like the long-range order. It is suggested that the pseudospin approach provides a single, systematic approximation scheme, not only for describing the magnetic properties of a class of solid free radicals, but also as a check for widely used many-body techniques.