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

We investigate the spin-1/2 Heisenberg star introduced by Richter and Voigt. The model is defined by H = J(1) Sigma(i=1)(N) S0Si + J(2)H(R)(S-i); J(1), J(2) greater than or equal to 0, i = 1,...,N In extension to the work of Richter and Voigt we consider a more general H-R(S-i) describing the properties of the spins surrounding the central spin 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 [S0Si] 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.