Completing Bethe's Equations at Roots of Unity

In a previous paper we demonstrated that Bethe's equations are not sufficient to specify the eigenvectors of the XXZ model at roots of unity for states where the Hamiltonian has degenerate eigenvalues. We here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the sl ₂ loop algebra symmetry is sufficiently powerful to determine that the highest weight of each irreducible representation is given by Bethe's ansatz.     

Transient field measurements of first-excited stateg-factors in188,190,192Os

Transient-field precessions were measured simultaneously for the 2₁ ⁺ states of^188,190,192Os as ions of these nuclei traversed a thin polarized iron foil. In contrast with most earlier measurements, the relative gyromagnetic ratios deduced here are independent of the level lifetimes. Emphasis is placed upon determination of theg-factor of the first excited state in¹⁹⁰Os, as disparities in measurements of the lifetimes of this level have led to uncertainties in itsg-factor.The cooperation and continued support of the staff of the Australian National Unversity Pelletron Laboratory is appreciated greatly. We would like to thank A.H.F. Muggleton for assistance with prepartion of the target, P.M. Davidson for aid during the experiment, and T.H. Heseltine for contributions to aspects of the analysis.     

Critical exponents of the Ising model on low-dimensional fractal media

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents β, γ, and ν are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_ef), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_ef=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.