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ZhETF, Vol. 131, No. 3, p. 511 (March 2007)
(English translation - JETP, Vol. 104, No. 3, p. 461, March 2007 available online at )

ISING MODELS ON THE 2\times2\times\infty LATTICES
Yurishchev M.A.

Received: October 19, 2006

PACS: 05.50.+q, 75.10.Hk, 75.40.Cx

DJVU (75.5K) PDF (263.9K)

Exact analytic solutions are presented for two 2\times2\times\infty Ising étagères. The first model has a simple cubic lattice with fully anisotropic interactions. The second model consists of two different types of linear chains and includes noncrossing diagonal bonds on the side faces of the 2\times2\times\infty parallelepiped. In both cases, the solutions are expressed through square radicals and obtained by using the obvious symmetry of the Hamiltonians, {\bf Z}_2\times{\bf C}_{2v}, and the hidden algebraic λλ symmetry of the transfer matrix secular equations. The solution found for the second model is used to analyze the behavior of specific heat in a frustrated many-chain system.

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