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.
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References
C. J. Thompson,J. Stat. Phys. 27:441 (1982).
C. J. Thompson,J. Stat. Phys. 27:457 (1982).
J. Vannimenus,Z. Phys. B 43:141 (1981).
M. E. Fisher,Physica 106A:28 (1981).
P. Bak and J. von Boehm,Phys. Rev. B 21:5297 (1980).
S. R. McKay, A. Nihat Berker, and S. Kirkpatrick,Phys. Rev. Lett. 48:767 (1982).
S. Inawashiro and C. J. Thompson,Phys. Lett. A, to be published.
S. Katsura and M. Takizawa,Prog. Theor. Phys. 51:82 (1974).
E. Müller-Hartmann and J. Zittartz,Phys. Rev. Lett. 33:893 (1974).
S. F. Edwards and P. W. Anderson,J. Phys. F. 5:965 (1975).
K. Kaneko,Prog. Theor. Phys. 68:669 (1982).
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Inawashiro, S., Thompson, C.J. & Honda, G. Ising model with competing interactions on a Cayley tree. J Stat Phys 33, 419–436 (1983). https://doi.org/10.1007/BF01009804
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DOI: https://doi.org/10.1007/BF01009804