An equivalence relation of boundary/initial conditions, and the infinite limit properties

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex model is classified through the density of left/down arrows on the boundary. The free energy becomes identical to that obtained by Lieb and Sutherland with the periodic boundary condition, if the density of the arrows is equal to 1/2. The relation to the structure of the transfer matrix and a relation to stochastic processes are noted.Comment: 6 pages with a figure, no change but the omitted figure is adde

The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model

In this paper a method previously employed by Salmhofer to establish an exact equivalence of the one-flavour strong coupling lattice Schwinger model with Wilson fermions to some 8-vertex model is applied to the case with two flavours. As this method is fairly general and can be applied to strong coupling QED and purely fermionic models with any (sufficiently small) number of Wilson fermions in any dimension the purpose of the present study is mainly a methodical one in order to gain some further experience with it. In the paper the vertex model equivalent to the two-flavour strong coupling lattice Schwinger model with Wilson fermions is found. It turns out to be some modified 3-state 20-vertex model on the square lattice, which can also be understood as a regular 6-state vertex model. In analogy with the one- flavour case, this model can be viewed as some loop model.Comment: 22 pages LaTe

Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model

We embody the density matrix renormalization group (DMRG) method for the 19-vertex model on a square lattice in order to investigate the Berezinskii-Kosterlitz-Thouless transition. Elements of the transfer matrix of the 19-vertex model are classified in terms of the total value of arrows in one layer of the square lattice. By using this classification, we succeed to reduce enormously the dimension of the matrix which has to be diagonalized in the DMRG method. We apply our method to the 19-vertex model with the interaction $K=1.0866$ and obtain $c=1.006(1)$ for the conformal anomaly. PACS. 05.90.+m, 02.70.-cComment: RevTeX style, 20 pages, 12 figure

Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain

We propose a set of nonlinear integral equations to describe on the excited states of an integrable the spin 1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study on the supersymmetric sine-Gordon model.Comment: 15 pages, 2 Figures, typos correcte

Yang-Baxter equation for the asymmetric eight-vertex model

In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis clarify the reason both manifolds need to share a universal invariant. We also show that the free-fermion condition implies three distinct classes of integrable models.Comment: Latex, 12 pages, 1 figur

Practical Techniques for Vision-Language Segmentation Model in Remote Sensing

Traditional semantic segmentation models often struggle with poor generalizability in zero-shot scenarios such as recognizing attributes unseen in the training labels. On the other hands, language-vision models (VLMs) have shown promise in improving performance on zero-shot tasks by leveraging semantic information from textual inputs and fusing this information with visual features. However, existing VLM-based methods do not perform as effectively on remote sensing data due to the lack of such data in their training datasets. In this paper, we introduce a two-stage fine-tuning approach for a VLM-based segmentation model using a large remote sensing image-caption dataset, which we created using an existing image-caption model. Additionally, we propose a modified decoder and a visual prompt technique using a saliency map to enhance segmentation results. Through these methods, we achieve superior segmentation performance on remote sensing data, demonstrating the effectiveness of our approach

The exact equivalence of the one-flavour lattice Thirring model with Wilson fermions to a two-colour loop model

Within Euclidean lattice field theory an exact equivalence between the one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$ to a two-colour loop model on the square lattice is established. For non-interacting fermions this model reduces to an exactly solved loop model which is known to be a free fermion model. The two-colour loop model equivalent to the Thirring model can also be understood as a 4-state 49-vertex model.Comment: 29 pages LaTe

Free Expansion of a Weakly-interacting Dipolar Fermi Gas

We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann and zero-temperature Thomas-Fermi gases in the Hartree-Fock and Landau-Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouville's theorem in the long-time behaviors of the both gases

Finite-dimensional analogs of string s <-> t duality and pentagon equation

We put forward one of the forms of functional pentagon equation (FPE), known from the theory of integrable models, as an algebraic explanation to the phenomenon known in physics as st duality. We present two simple geometrical examples of FPE solutions, one of them yielding in a particular case the well-known Veneziano expression for 4-particle amplitude. Finally, we interpret our solutions of FPE in terms of relations in Lie groups.Comment: LaTeX, 12 pages, 6 eps figure

Explicit formulas for the generalized Hermite polynomials in superspace

We provide explicit formulas for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace. The construction relies on the triangular action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions.Comment: 19 pages. This is a recasting of the second part of the first version of hep-th/0305038 which has been splitted in two articles. In this revised version, the introduction has been rewritten and a new appendix has been added. To appear in JP