On Next-Nearest-Neighbor Interaction in Linear Chain. II

Continuing our work on the ground-state properties of the Hamiltonian H=12J ∑ i=1N σi·σi+1 + 12Jα ∑ i=1N σi·σi+2, −1≤α≤1,we have completed the study of 10 spins. The results of short-chain calculations provide better upper and lower bounds of the ground-state energy per particle as N → ∞, but no simple formula can be fitted to the data to get this limit for all α. For J 0 and α = ½, however, this is exactly found to be −¾J. Some upper and lower bounds for the free energy are also derived.