Abstract
The commutativity of the 1-dimensional XY-h type Hamiltonian and the transfer matrix of a 2-dimensional spin-lattice model constructed from an R-matrix is studied by Sutherland's method. We generalize Krinsky's result to more general Hamiltonians and more general R matrices, and we obtain a generic condition on their parameters for the commutativity, which defines an irreducible algebraic manifold in the parameter space.
Similar content being viewed by others
References
H. Araki and T. Tabuchi, “On commuting transfer matrices,”Helv. Phys. Acta 69, 717–751 (1996).
S. Krinsky, “Equivalence of the free Fermion model to the ground state of the linearXY model,”Phys. Lett. 39A, 169–170 (1972).
B. Sutherland, “Two-dimensional hydrogen-bonded crystals without the ice rule,”J. Math. Phys.,11, 3183–3186 (1970).
T. Tabuchi, “Generalizations of Sutherland's commutativity proof and Felderhof's parametrization for the 8-vertex model,” in preparation.
H. Araki, “Master symmetries of theXY-model,”Commun. Math. Phys. 132, 155–176 (1990).
C. Fan and F. Y. Wu, “General lattice model of phase transitions,”Phys. Rev. B2, 723–733 (1970).
H. Araki and T. Tabuchi, “Generalization of Krinsky's commutativity proof of transfer matrices with Hamiltonians II,” in preparation.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Araki, H., Tabuchi, T. Generalization of Krinsky's commutativity proof of transfer matrices with Hamiltonians. Found Phys 27, 1485–1494 (1997). https://doi.org/10.1007/BF02551495
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02551495