J. Douthett et R. Krantz, ENERGY EXTREMES AND SPIN CONFIGURATIONS FOR THE ONE-DIMENSIONAL ANTIFERROMAGNETIC ISING-MODEL WITH ARBITRARY-RANGE INTERACTION, Journal of mathematical physics, 37(7), 1996, pp. 3334-3353
The one-dimensional antiferromagnetic spin-1/2 Ising model is investig
ated using the formalism of Maximally/Minimally Even sets. The salient
features of Maximally/Minimally Even set theory are introduced. Energ
y and spin content vectors are defined to facilitate the use of interv
al spectra used in Maximally/Minimally Even set theory. It is shown th
at Maximally Even sets of up- and down-spins minimize the configuratio
nal energy per spin and that Minimally Even sets maximize configuratio
nal energy per spin. An exponentially decreasing antiferromagnetic pai
rwise interaction of arbitrary range is used as an example interaction
. The asymptotic (N-->infinity) configurational energy per spin and th
e energy per spin calculated for seven-near neighbors are compared. (C
) 1996 American Institute of Physics.