Algebraic reduction of the Ising model

Details Algebraic reduction of the Ising model Algebraic reduction of the Ising model

2008-03-28

arxiv.org/abs/0803.4036v3

J. Stat. Phys. 132, 959 (2008)

Physics

Condensed Matter

Statistical Mechanics

25 pages, one figure, last reference completed. Various typos fixed. Changes on 12 July 2008: Fig 1, 0 to +1; before (2.1), if

Scientific paper

10.1007/s10955-008-9587-y

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.

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