The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.

We investigate the Z(2) gauge model on a generalized Bethe lattice in the presence of a three-plaquette interaction. We obtain a cascade of phase transitions according to the Feigenbaum scheme leading to chaotic states for some values of parameters of the model. The duality between this gauge model and the three-site Ising spin model on the Husimi tree is shown. The Lyapunov exponents as new or...

The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.

A bstract We introduce new classes of integrable models that exhibit a structure similar to flag vector spaces. present their Hamiltonians, R -matrices and Bethe-ansatz solutions. These have type generalized graded algebra symmetry.

The mean-square end-to-end distance of an N-step polymer on a Bethe lattice is calculated. We consider semiflexible polymers placed on isotropic and anisotropic lattices. The distance on the Cayley tree is defined by embedding the tree on a sufficiently high-dimensional Euclidean space, considering that every bend of the polymer defines a direction orthogonal to all the previous ones. In the is...

The one-dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric point by means of Bethe ansatz. Following Sutherland’s previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. ...

The Bethe approximation, or loopy belief propagation algorithm, is a successful method for approximating partition functions of probabilistic models associated with graphs. Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while the other terms are labeled b...