We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian Y (Xr) or its quantum affine analogue Uq(X (1) r ) for Xr = Br, Cr and Dr. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of Y (Xr). Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conj...

The Bethe ansatz approach for factorizable centrally extended su(2|2) S-matrices Abstract We consider the Bethe ansatz solution of integrable models interacting through factor-ized S-matrices based on the central extention of the su(2|2) symmetry. The respective su(2|2) R-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. Th...

Electron-impact total ionization cross sections for the CH radical and C2H2 (acetylene) have been calculated using the Binary-Encounter-Bethe (BEB) model. The BEB model combines the Mott cross section and the asymptotic form of the Bethe theory, and has been shown to generate reliable ionization cross sections for a large variety of molecules. The BEB cross sections for CH and C2H2 are in good ...

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstat...

We present an algebraic Bethe ansatz for certain submanifolds of the bilayer vertex models proposed by Shiroishi and Wadati as coupled asymmetric six-vertex free-fermion models. A peculiar feature of our formulation is the presence of a diagonal monodromy matrix element that does not generate unwanted terms. The model contains two free-parameters entering into the Bethe ansatz equations as a pu...

We outline the relationship between the thermodynamic densities and quasi-particle descriptions of spectra of RSOS models with an underlying Bethe equation. We use this to prove completeness of states in some cases and then give an algorithm for the construction of branching functions of their emergent conformal field theories. Starting from the Bethe equations of Dn type, we discuss some aspec...

The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain polynomials. We also show that the corresponding transfer matrix eigenvalues agree. PACS: 05.50.+q, 71.10.Fd, 71.10.Pm †e-mail: [email protected]...

The phase transition of two-dimensional Ising model on random point patterns is investigated using Monte Carlo simulation and the critical temperature is calculated using the Bethe approximation. We find a linear relation between the critical temperature and the structural characteristics of the random point pattern, as described by Aboav's parameter. Numerical results and analytical calculatio...

We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has Uq(SU(3)) symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 32 which is the exponent corresponding to KPZ growt...

One-dimensional repulsive δ-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of p...