ISSN:
1572-9613
Keywords:
One-dimensional Ising chain
;
competing interactions
;
ground state degeneracy
;
Fibonacci sequence
;
close packing of dimers
;
directed self-avoiding walks
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ 1, and akth neighboranti-ferromagnetic interactionJ k . WhenJ k/J1=−1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k−1)th term in a generalized Fibonacci sequence defined by,F N (k) =F N−1 (k) +F N−k (k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2×∞ strip of the square lattice, and (c) “directed” self-avoiding walks on finite lattice strips.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01008476
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