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 $H=J_1 \sum_{i=1}^{N}{{\bf s}_0{\bf s}_i} + J_2 H_{R}\{{\bf s}_i\}$ ; $J_1,J_2 \ge 0$ , $i=1,...,N$. In extension to the Ref. we consider a more general $H_{R}\{{\bf s}_i\}$ describing the properties of the spins surrounding the central spin ${\bf s}_0$. 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 $\langle {\bf s}_0{\bf s}_i \rangle$ 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.