Some properties of frustrated spin systems: extensions and applications of Lieb-Schupp approach

Lieb and Schupp have obtained, using certain version of ``spin-reflection positivity'' method, a number of ground-state properties for frustrated Heisenberg models. One group of these results is related to singlet nature of ground state and it needs an assumption of reflection symmetry present in the system. In this paper, it is shown that the result holds also for other symmetries (inversion etc.). The second Lieb-Schupp result is relation between ground-state energies of certain systems. In the paper, this relation is applied to multidimensional models on various lattices.Comment: 15 pages, 8 eps figures, revtex

The Educational Achievement of U.S. Puerto Ricans

With longitudinal data, this article extends to the 1990s research on minority educational achievement and emphasizes the experiences of Puerto Ricans. The authors\u27 results suggest that compared with whites, blacks, and Mexicans, Puerto Ricans exhibit the lowest high school graduation rates and that their educational disadvantage is unique. Even if Puerto Ricans assumed the attributes of whites, they would graduate at lower rates than the latter. This finding, which has serious implications, deserves priority in the agendas of scholars and policy specialists alike