Abstract
Exact analytic solutions are presented for two 2 × 2 × ∞ 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 × 2 × ∞ parallelepiped. In both cases, the solutions are expressed through square radicals and obtained by using the obvious symmetry of the Hamiltonians, Z 2 × 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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