Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Vertex Type Fractions of the Six-Vertex Model atΔ=-1

Таичиро Такаги

Published Aug 15, 1998• 0 citations
Publisher

Abstract

We study analytic expressions for the averaged fraction of each vertex type of the six-vertex model extensively. Upon the critical line the expressions of the quantity in the anti-ferroelectric phase and in the gapless phase get simplified. This enables us to see more easily the equivalence of the two quantities of which one is derived by differentiating the free energy, and the other is by calculating a trace of the vertex operators in the theory of a quantum affine algebra. We also prove an extra liner relation satisfied by the fractions on the critical line.

DOI
10.1143/jpsj.67.2653

Related papers

Integral Representation of the Correlations around a Vertex of the Six-Vertex Model

Таичиро Такаги

We study exact solutions of the four-point correlation functions around a vertex of the anti-ferroelectric six-vertex model. After showing that an expression for the correlations is readily obtained by differentiating the known exact solution of the free energy, we present a new expression for the correlations derived through the recently developed vertex operator approach. It has the form of a double contour integral of a meromorphic function. To give a new verification of the vertex operator approach beyond the case of the one-point function, we prove the equality of the two expressions by calculating the contour integrals.

Journal of the Physical Society of Japan•Jul 15, 1996•2 citations

Introduction to solvable lattice models in statistical and mathematical physics

Tetsuo Deguchi

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears. We discuss the connection of the six-vertex model to the conformal field theory with c=1. We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models. We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group. The graphical approach is emphasized in this review. We explain the meaning of the Yang-Baxter equation by its diagram. Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation. We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models. As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.

arXiv:cond-mat/0304309•Apr 14, 2003•0 citations

Introduction to solvable lattice models in statistical and mathematical physics

Tetsuo Deguchi

Some features of integrable lattice models are reviewed for the case of the six-vertex model.By the Bethe ansatz method we derive the free energy of the six-vertex model.Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears.We discuss the connection of the six-vertex model to the conformal field theory with c = 1.We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models.We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group.The graphical approach is emphasized in this review.We explain the meaning of the Yang-Baxter equation by its diagram.Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation.We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models.As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.

Institute of Physics eBooks•Nov 26, 2004•3 citations

Introduction to solvable lattice models in statistical and mathematical physics

Tetsuo Deguchi

Some features of integrable lattice models are reviewed for the case of the six-vertex model.By the Bethe ansatz method we derive the free energy of the six-vertex model.Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears.We discuss the connection of the six-vertex model to the conformal field theory with c = 1.We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models.We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group.The graphical approach is emphasized in this review.We explain the meaning of the Yang-Baxter equation by its diagram.Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation.We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models.As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.

Taylor & Francis eBooks•Sep 1, 2003•8 citations

Algebraic analysis of solvable lattice models

道夫 神保, 哲二 三輪

Background of the problem The spin $1/2$ XXZ model for $\Delta <-1$ The six-vertex model in the anti-ferroelectric regime Solvability and symmetry Correlation functions-physical derivation Level one modules and bosonization Vertex operators Space of states-mathematical picture Traces of vertex operators Correlation functions and form factors The $XXX$ limit $q\rightarrow-1$ Discussions List of formulas.

American Mathematical Society eBooks•Jan 1, 1999•1 citation

Integral Representation of the Internal Energy of theFModel

Таичиро Такаги

We give an integral representation of the internal energy of the F model, a special case of the anti-ferroelectric six-vertex model. This representation is obtained naturally as a trace function of the vertex operators. We also take the critical limit of our expression and find that it reproduces Lieb's result of the internal energy at T c .

Journal of the Physical Society of Japan•Apr 15, 1996•3 citations
We study analytic expressions for the averaged fraction of each vertex type of the six-vertex model extensively. Upon the critical line the expressions of the quantity in the anti-ferroelectric phase and in the gapless phase get simplified. This enables us to see more easily the equivalence of the two quantities of which one is derived by differentiating the free energy, and the other is by calculating a trace of the vertex operators in the theory of a quantum affine algebra. We also prove an extra liner relation satisfied by the fractions on the critical line.
We study exact solutions of the four-point correlation functions around a vertex of the anti-ferroelectric six-vertex model. After showing that an expression for the correlations is readily obtained by differentiating the known exact solution of the free energy, we present a new expression for the correlations derived through the recently developed vertex operator approach. It has the form of a double contour integral of a meromorphic function. To give a new verification of the vertex operator approach beyond the case of the one-point function, we prove the equality of the two expressions by calculating the contour integrals.
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears. We discuss the connection of the six-vertex model to the conformal field theory with c=1. We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models. We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group. The graphical approach is emphasized in this review. We explain the meaning of the Yang-Baxter equation by its diagram. Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation. We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models. As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.
Some features of integrable lattice models are reviewed for the case of the six-vertex model.By the Bethe ansatz method we derive the free energy of the six-vertex model.Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears.We discuss the connection of the six-vertex model to the conformal field theory with c = 1.We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models.We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group.The graphical approach is emphasized in this review.We explain the meaning of the Yang-Baxter equation by its diagram.Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation.We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models.As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.
Some features of integrable lattice models are reviewed for the case of the six-vertex model.By the Bethe ansatz method we derive the free energy of the six-vertex model.Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears.We discuss the connection of the six-vertex model to the conformal field theory with c = 1.We also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models.We show that the six-vertex model has rich mathematical structures such as the quantum groups and the braid group.The graphical approach is emphasized in this review.We explain the meaning of the Yang-Baxter equation by its diagram.Furthermore, we can understand the defining relation of the algebraic Bethe ansatz by the graphical representation.We can thus easily translate formulas of the algebraic Bethe ansatz into those of the statistical models.As an illustration, we show explicitly how we can derive Baxter's expressions from those of the algebraic Bethe ansatz.
Background of the problem The spin 1/21/21/2 XXZ model for Δ<−1\Delta <-1Δ<−1 The six-vertex model in the anti-ferroelectric regime Solvability and symmetry Correlation functions-physical derivation Level one modules and bosonization Vertex operators Space of states-mathematical picture Traces of vertex operators Correlation functions and form factors The XXXXXXXXX limit q→−1q\rightarrow-1q→−1 Discussions List of formulas.