Journal article

Ising model with competing interactions on a Cayley tree

S Inawashiro, CJ Thompson, G Honda

Journal of Statistical Physics | Published : 1983

Abstract

An iterative scheme is developed for a renormalized effective nearest-neighbor coupling Kr and effective field per site Kr for spins in the rth shell of a Cayley tree with nearest neighbor J, and next nearest neighbor J′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range of J'/J < 0 values where Xr, and Kr iterate to a continuous or quasicontinuous attractor in the X-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases. © 1983 Plenum Publishing Corpor..

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