Last updates: 6 December 2011
Lattice models and Transfer matrices
Let be a vector space with basis
be a vector space with basis .
The Boltzmann weights are the matrix entries
of an operator .
The monodromy matrix is
The transfer matrix is
- The Hamiltonian is
- The partition function on an
As operators on ,
and this implies that, as operators on
Multiplying on the left by
Remark: In many applications
and the quantum Yang-Baxter equation (QYBE) gives
with gives (1.1).
Notes and References
This page is based on section 5.2 of [dG]. The formula ??? appears as
??? in [TF] who quote [Bax].
R. Baxter, One-dimensional anisotropic Heisenberg chain,
Ann. Phys. 70 (1972), 323-337.
J. de Gier,
Random Tilings and Solvable Lattice Models,
Ph.D Thesis, University of Amsterdam, 1998.
L.A. Takhtajan and L.D. Faddeev,
The quantum method of the inverse problem and the Heisenberg XYZ model,
Russian Math Surveys 34 5 (1979), 11-68.