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

Abstract

Continuing our work on the ground‐state properties of the Hamiltonian $$\mathrm{H=}\frac{1}{2}J{\displaystyle \sum _{\text{i=1}}^N}{\sigma }_i{\mathrm{·\sigma }}_{\text{i+1}}+\frac{1}{2}\mathrm{J\alpha }{\displaystyle \sum _{\text{i=1}}^N}{\sigma }_i{\mathrm{·\sigma }}_{\text{i+2}}\text{,\hspace{0.17em}−1≤α≤1}$$ , 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.