Inequalities between ground-state energies of Heisenberg models
  The Lieb-Schupp inequality is the inequality between ground state en- ergies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture. 
Jacek Wojtkiewicz and Rafa{\l} Skolasi\'nski
math-ph cond-mat.str-el math.MP