  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.
