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Journal of Magnetism and Magnetic Materials

One-dimensional Ising system with arbitrary interactions

Norikiyo Uryû, Mitsuru Tanimura

Published Feb 1, 1986• 0 citations
Publisher
DOI
10.1016/0304-8853(86)90808-5

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The concept of the irreducible block is introduced for the one-dimensional Ising system with an arbitrary interaction of finite range. It is proved that the ground state energy of the system occurs for a regular chain of one of the irreducible blocks or for coexistence of the regular chains of the irreducible blocks. It is shown that the ground state energy of the linear Ising magnet with pair interactions up to third neighbours is effected by the seven spin orderings recently given for the case of spin 1 / 2 by Katsura and Narita (1973), and that the ground state energy of the Ising magnet of spin larger than 1 / 2 is effected by the same set of orderings as for the corresponding Ising magnet of spin 1 / 2 .