Exact Results for the Adsorption of a Flexible Self-Avoiding Polymer Chain in Two Dimensions

We derive the exact critical couplings ($x^*, y_{\rm a}^*$), where $y_{\rm a}^*/x^* = \sqrt{1+\sqrt2} = 1.533\ldots\,$, for the polymer adsorption transition on the honeycomb lattice, along with the universal critical exponents, from the Bethe Ansatz solution of the O($n$) loop model at the special transition. Our result for the thermal scaling dimension, and thus the crossover exponent $\phi=\frac{1}{2}$, is in agreement with an earlier result based on conformal invariance arguments. Our result for the geometric scaling dimensions confirms recent conjectures that they are given by $h_{\ell+1,3}$ in the Kac formula.Comment: 11 pages, REVTEX. Minor corrections made and a new reference added to the O(n) model with mixed boundary conditions - final version for publication in Physical Review Letter

Diagonal KK-matrices and transfer matrix eigenspectra associated with the G2(1)G^{(1)}_2 RR-matrix

We find all the diagonal $K$-matrices for the $R$-matrix associated with the minimal representation of the exceptional affine algebra $G^{(1)}_2$. The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe ansatz. We find many similarities with the case of the Izergin-Korepin $R$-matrix associated with the affine algebra $A^{(2)}_2$.Comment: 11 pages, LaTe

Exactly solvable quantum spin tubes and ladders

We find families of integrable n-leg spin-1/2 ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su(N) spin chains with N=2^n. Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are n-dependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe Ansatz.Comment: 6 pages, Latex, 1 eps fig, to appear in J. Phys.

Excitations in the dilute A_L lattice model: E_6, E_7 and E_8 mass spectra

On the basis of features observed in the exact perturbation approach solution for the eigenspectrum of the dilute A_3 model, we propose expressions for excitations in the dilute A_4 and A_6 models. Principally, we require that these expressions satisfy the appropriate inversion relations. We demonstrate that they give the expected E_7 and E_6 mass spectra, and universal amplitudes, and agree with numerical expressions for the eigenvalues.Comment: 16 pages, Latex, Elsevier style file

Ferromagnetic behaviour in the strongly interacting two-component Bose gas

We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat $c_v \sim T^{1/2}$ and the susceptibility $\chi \sim T^{-2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.Comment: 15 pages, 6 figures, revised version, references added, minor correction