The spin 1/2 Heisenberg star with frustration II: The influence of the embedding medium

Abstract

We investigate the spin 1/2 Heisenberg star introduced in J. Richter and A. Voigt, J. Phys. A: Math. Gen. {\bf 27}, 1139 (1994). The model is defined by $H=J_1{\sum }_{i=1}^N{\mathbf{s}}_0{\mathbf{s}}_i+J_2{H}_R\{{\mathbf{s}}_i\}$ ; $J_1,J_2\ge 0$ , $i=1,...,N$. In extension to the Ref. we consider a more general $H_R\{{\mathbf{s}}_i\}$ describing the properties of the spins surrounding the central spin ${\mathbf{s}}_0$. The Heisenberg star may be considered as an essential structure element of a lattice with frustration (namely a spin embedded in a magnetic matrix $H_R$) or, alternatively, as a magnetic system $H_R$ with a perturbation by an extra spin. We present some general features of the eigenvalues, the eigenfunctions as well as the spin correlation $⟨{\mathbf{s}}_0{\mathbf{s}}_i⟩$ of the model. For $H_R$ being a linear chain, a square lattice or a Lieb-Mattis type system we present the ground state properties of the model in dependence on the frustration parameter $\alpha =J_2/J_1$. Furthermore the thermodynamic properties are calculated for $H_R$ being a Lieb--Mattis antiferromagnet.

16 pages, uuencoded compressed postscript file, accepted to J. Phys. A: Math. Gen