ISSN:
1572-9613
Keywords:
Cayley tree
;
iteration
;
fixed points
;
cycles
;
attractors
;
chaos
;
spin glass
;
frequency locking
;
devil's staircase
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK r and effective field per siteK r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J 〈 0 values whereX r, and Kr iterate to a continuous or quasicontinuous attractor in theX-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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01009804
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