Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties

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 \alpha_s of the Kashiwara-Miwa model is given and satisfies the scaling relation \alpha_b=2\alpha_s-2, where \alpha_b is the bulk exponent.Comment: 17 pages, no ps figures, latex fil

Fusion Hierarchy and Finite-Size Corrections of Uq[sl(2)]U_q[sl(2)] Invariant Vertex Models with Open Boundaries

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the $su$(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group $U_q[sl(2)]$. In the case of the parameter $q^h=-1$ ($h=4,5,\cdots$) the functional relations in the limit of spectral parameter u\to \i\infty are truncated. This shows that the $su$(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition.Comment: Pages 29; revised versio

SOLUTION OF FUNCTIONAL EQUATIONS OF RESTRICTED An−1(1)A_{n-1}^{(1)} FUSED LATTICE MODELS

Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted $A_{n-1}^{(1)}$ lattice models of Jimbo, Miwa and Okado. Specifically, these equations are solved analytically for the finite-size scaling spectra, central charges and some conformal weights. The results are obtained in terms of Rogers dilogarithm and correspond to coset conformal field theories based on the affine Lie algebra $A_{n-1}^{(1)}$ with GKO pair $A^{(1)}_{n-1}\; \oplus A^{(1)}_{n-1}\;\supset \; A^{(1)}_{n-1}$.Comment: 25 pages;latex file(epic.tex needed);Res.Rep.No 39;Tex Prob. fixed

Algebraic Bethe ansatz for the supersymmetric t−Jt-J model with reflecting boundary conditions

In the framework of the graded quantum inverse scattering method (QISM), we obtain the eigenvalues and eigenvectors of the supersymmetric $t-J$ model with reflecting boundary conditions in FFB background. The corresponding Bethe ansatz equations are obtained.Comment: Latex file, 23 Page

Surface Critical Phenomena and Scaling in the Eight-Vertex Model

We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain the exact surface free energy from a crossing-unitarity relation. The singular part of the surface energy is described by the critical exponents $\alpha_s = 2 - \frac{\pi}{2\mu}$ and $\alpha_1 = 1 - \frac{\pi}{\mu}$, where $\mu$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $\mu=\pi/2$ and confirm the scaling relations $\alpha_s = \alpha_b + \nu$ and $\alpha_1 = \alpha_b -1$.Comment: 12 pages, LaTeX with REVTEX macros needed. To appear in Physical Review Letter

Visual characterization of associative quasitrivial nondecreasing operations on finite chains

In this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains. We also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains. Finally, we estimate the number of functions belonging to the previous classes.Comment: 25 pages, 18 Figure

Two Magnetic Impurities with Arbitrary Spins in Open Boundary t-J Model

From the open boundary t-J model, an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in details. We discuss also the string solutions of the Bethe ansatz equations, which describe the bound states of the charges and spins. By minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz equations. The finite size correction of the free energy contributed by the magnetic impurities is obtained explicitly. The properties of the system at some special limits are discussed and the boundary bound states are obtained.Comment: 18 pages, Revte

Solutions of the reflection equations for the Uq[G2]U_q[G_2] vertex model

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half are non-diagonal. The latter are parameterized by two continuous parameters but only one solution has all entries non-null. The non-diagonal solutions do not reduce to diagonal ones at any special limit of the free-parameters.Comment: 18 page

The density of macrophages in the invasive front is inversely correlated to liver metastasis in colon cancer

<p>Abstract</p> <p>Background</p> <p>Although an abundance of evidence has indicated that tumor-associated macrophages (TAMs) are associated with a favorable prognosis in patients with colon cancer, it is still unknown how TAMs exert a protective effect. This study examined whether TAMs are involved in hepatic metastasis of colon cancer.</p> <p>Materials and methods</p> <p>One hundred and sixty cases of pathologically-confirmed specimens were obtained from colon carcinoma patients with TNM stage IIIB and IV between January 1997 and July 2004 at the Cancer Center of Sun Yat-Sen University. The density of macrophages in the invasive front (CD68TF_Hotspot) was scored with an immunohistochemical assay. The relationship between the CD68TF_Hotspotand the clinicopathologic parameters, the potential of hepatic metastasis, and the 5-year survival rate were analyzed.</p> <p>Results</p> <p>TAMs were associated with the incidence of hepatic metastasis and the 5-year survival rate in patients with colon cancers. Both univariate and multivariate analyses revealed that the CD68TF_Hotspotwas independently prognostic of survival. A higher 5-year survival rate among patients with stage IIIB after radical resection occurred in patients with a higher macrophage infiltration in the invasive front (81.0%) than in those with a lower macrophage infiltration (48.6%). Most importantly, the CD68TF_Hotspotwas associated with both the potential of hepatic metastasis and the interval between colon resection and the occurrence of hepatic metastasis.</p> <p>Conclusion</p> <p>This study showed evidence that TAMs infiltrated in the invasive front are associated with improvement in both hepatic metastasis and overall survival in colon cancer, implying that TAMs have protective potential in colon cancers and might serve as a novel therapeutic target.</p