On NextNearestNeighbor Interaction in Linear Chain. II
Abstract
Continuing our work on the groundstate properties of the Hamiltonian H=1/2J ∑ i=1N σ_{i}.σ_{i+1} + 1/2Jα ∑ i=1N σ_{i}.σ_{i+2}, 1≤α≤1, we have completed the study of 10 spins. The results of shortchain calculations provide better upper and lower bounds of the groundstate 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 August 1969
 DOI:
 10.1063/1.1664979
 Bibcode:
 1969JMP....10.1399M