Analytical results for the Coqblin-Schrieffer model with generalized magnetic fields

Using the approach alternative to the traditional Thermodynamic Bethe Ansatz, we derive analytical expressions for the free energy of Coqblin-Schrieffer model with arbitrary magnetic and crystal fields. In Appendix we discuss two concrete examples including the field generated crossover from the SU(4) to the SU(2) symmetry in the SU(4)-symmetric model.Comment: 5 page

Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov τ2\tau_2-model for N=2

We find a representation of the row-to-row transfer matrix of the Baxter-Bazhanov-Stroganov $\tau_2$-model for N=2 in terms of an integral over two commuting sets of grassmann variables. Using this representation, we explicitly calculate transfer matrix eigenvectors and normalize them. It is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain Toeplitz matrices.Comment: 23 page

Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q^2=-1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.Comment: 20 pages, 6 figures, to appear in J. Phys. A: Math. and Ge

Coherent spin relaxation in molecular magnets

Numerical modelling of coherent spin relaxation in nanomagnets, formed by magnetic molecules of high spins, is accomplished. Such a coherent spin dynamics can be realized in the presence of a resonant electric circuit coupled to the magnet. Computer simulations for a system of a large number of interacting spins is an efficient tool for studying the microscopic properties of such systems. Coherent spin relaxation is an ultrafast process, with the relaxation time that can be an order shorter than the transverse spin dephasing time. The influence of different system parameters on the relaxation process is analysed. The role of the sample geometry on the spin relaxation is investigated.Comment: Latex file, 22 pages, 7 figure

Universal integrability objects

We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional relations correcting inexactitudes of the previous considerations. A special attention is given to the connection of the representations used to construct the universal transfer operators and $Q$-operators.Comment: 21 pages, submitted to the Proceedings of the International Workshop "CQIS-2012" (Dubna, January 23-27, 2012

Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.Comment: 14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007

Analytical Bethe Ansatz for A2n−1(2),Bn(1),Cn(1),Dn(1)A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n quantum-algebra-invariant open spin chains

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras $A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n$, and which have the quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$, respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is removed

Integrable Circular Brane Model and Coulomb Charging at Large Conduction

We study a model of 2D QFT with boundary interaction, in which two-component massless Bose field is constrained to a circle at the boundary. We argue that this model is integrable at two values of the topological angle, $\theta =0$ and $\theta=\pi$. For $\theta=0$ we propose exact partition function in terms of solutions of ordinary linear differential equation. The circular brane model is equivalent to the model of quantum Brownian dynamics commonly used in describing the Coulomb charging in quantum dots, in the limit of small dimensionless resistance $g_0$ of the tunneling contact. Our proposal translates to partition function of this model at integer charge.Comment: 20 pages, minor change

Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation

Whilst many solutions have been found for the Quantum Yang-Baxter Equation (QYBE), there are fewer known solutions available for its higher dimensional generalizations: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and Moore's simplex equation (FME). In this paper, we present families of solutions to FME which may help us to understand more about higher dimensional generalization of QYBE.Comment: LaTeX file. Require macros: cite.sty and subeqnarray.sty to process. To appear in J. Phys. A: Math. and Ge

Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model

We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the Wu-Kadanoff duality between the cube and vertex type tetrahedron equations is obtained explicitly for the Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by considering the symmetry property of the weight function, which is corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube. And we write down the symmetry relations of the weight functions under the actions of the symmetry group $G$ of the cube. The six angles with a constrained condition, appeared in the tetrahedron equation, can be regarded as the six spectrums connected with the six spaces in which the vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29