177 research outputs found
Elliptic solution for modified tetrahedron equations
As is known, tetrahedron equations lead to the commuting family of
transfer-matrices and provide the integrability of corresponding
three-dimensional lattice models. We present the modified version of these
equations which give the commuting family of more complicated two-layer
transfer-matrices. In the static limit we have succeeded in constructing the
solution of these equations in terms of elliptic functions.Comment: 11 page
Finite Size XXZ Spin Chain with Anisotropy Parameter
We find an analytic solution of the Bethe Ansatz equations (BAE) for the
special case of a finite XXZ spin chain with free boundary conditions and with
a complex surface field which provides for symmetry of the
Hamiltonian. More precisely, we find one nontrivial solution, corresponding to
the ground state of the system with anisotropy parameter
corresponding to . With a view to establishing an exact
representation of the ground state of the finite size XXZ spin chain in terms
of elementary functions, we concentrate on the crossing-parameter
dependence around for which there is a known solution. The
approach taken involves the use of a physical solution of Baxter's t-Q
equation, corresponding to the ground state, as well as a non-physical solution
of the same equation. The calculation of and then of the ground state
derivative is covered. Possible applications of this derivative to the theory
of percolation have yet to be investigated. As far as the finite XXZ spin chain
with periodic boundary conditions is concerned, we find a similar solution for
an assymetric case which corresponds to the 6-vertex model with a special
magnetic field. For this case we find the analytic value of the ``magnetic
moment'' of the system in the corresponding state.Comment: 12 pages, latex, no figure
Generalized Yang-Baxter Equation
A generalization of the Yang-Baxter equation is proposed. It enables to
construct integrable two-dimensional lattice models with commuting two-layer
transfer matrices, while single-layer ones are not necessarily commutative.
Explicit solutions to the generalized equations are found. They are related
with Botzmann weights of the chiral Potts model.Comment: 13 pages, TeX file. IHEP-93-?
- …