Dimers on a Rectangular Lattice

Baxter, R.J.

doi:10.1063/1.1664623

Dimers on a Rectangular Lattice

R.J. Baxter

Apr 1, 1968

Published in:

J.Math.Phys. 9 (1968) 4, 650

Published: Apr 1, 1968

DOI:

10.1063/1.1664623

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Abstract: (AIP)

A set of matrix equations is derived which yields the statistical mechanical properties of a system of monomers and dimers on a rectangular lattice in the thermodynamic limit. As the matrices are strictly of infinite dimensionality, the equations cannot be solved directly, but if they are restricted to be of finite and quite small dimensionality, very good approximations to the thermodynamic properties are obtained.

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[1]

P.W. Kasteleyn

- J.Math.Phys. 4 (1963) 287

[2]

P.W. Kasteleyn

- Physica 27 (1961) 1209

[3]

H.N.V. Temperley
,
M.E. Fisher

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Statistical Mechanics of Dimers on a Plane Lattice

Michael E. Fisher
(
- King's Coll. London
)

- Phys.Rev. 124 (1961) 1664-1672
•
DOI:
- 10.1103/PhysRev.124.1664

[4]

E.H. Lieb

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[5]

If this choice of y does happen to be orthogonal to the eigenvector x, there are an infinite number of other ways of choosing y so that x is of the form (3.3)