ENERGY EXTREMES AND SPIN CONFIGURATIONS FOR THE ONE-DIMENSIONAL ANTIFERROMAGNETIC ISING-MODEL WITH ARBITRARY-RANGE INTERACTION

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.