arXiv subjects
Publications and source records attributed to Y. -K. Zhou.
The boundary Boltzmann weights are found by solving the boundary star-triangle relations for the Fateev-Zamolodchikov and Kashiwara-Miwa models. We calculate the surface free energies of the models. The critical surface exponent α_s of the Kashiwara-Miwa model is given and satisfies the scaling relation α_b=2α_s-2, where α_b is the bulk exponent.
We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation. The models considered are related to the affine Lie algebras A_1^{(1)}, B_n^{(1)},C_n^{(1)} and D_n^{(1)}. The bulk and surface specific heat exponents are seen to satisfy the scaling relation 2α_s = α_b + 2. It follows from scaling relations that in regime III the correlation length exponent νis given by ν=(l+g)/2g, where l is the level and g is the dual Coxeter number. In regime II we find ν=(l+g)/2l.
As the new results for the massive Thirring model the L-matrix and the algebraic relations for its action angle variables are given. So it is shown most directly that this model which describes self-interacting relativistic Fermions in one-dimensional space is a quantum integrable system.
The analytic, nonlinear integral equation approach is used to calculate the finite-size corrections to the transfer matrix eigen-spectra of the critical dilute O(n) model on the square periodic lattice. The resulting bulk conformal weights extend previous exact results obtained in the honeycomb limit and include the negative spectral parameter regimes. The results give the operator content of the 19-vertex Izergin-Korepin model along with the conformal weights of the dilute $A_L$ face models in all four regimes.
The integrable quantum group $spl_q(2,1)$-invariant supersymmetric t-J model with open boundaries is studied via an analytic treatment of the Bethe equations. An $su(2)$ feature is seen to hold for states at or close to half-filling. For these states the eigenvalues of the transfer matrix of the t-J model satisfy a set of $su(2)$ functional relations. The finite-size corrections to the relevant eigenvalues, and thus the surface effect on the spin excitations, have been calculated analytically by solving the functional relations.