The Statistics of Honeycomb and Triangular Lattice. I.

概要

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After the matrix method in crystal statistics was introduced by R. Kubo^(1) Kramers and Wannier^(2), and others, Onsager^(3), using the abstract algebraic method, got the exact solution in the case of plane square net. His rather complicated method was simplified by Nambu^(6) considerably. We, independenty, attained the simplification of Onsager's method and have applied to the honeycomb lattice. And the exact solution has been obtained. From this, by the so called dual transformation we can get the partition function for triangular net. The Curie point occurs at ch 2H=2 in the honeycomb lattice and at exp (4H)=3 in the triangular net. These coincide with the resnlts obtained by the dual and star-triangle transformations^(4). The specific heat becomes logarithmically infinite but the energy itself remains continuous at this temperature. In the antiferromagnetic case, the honeycomb lattice behaves similar to the former case but the triangular net exhibits no phase change.
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