Figure - available from: Journal of Physics A: Mathematical and Theoretical
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Two-dimensional lattice on which the models are defined. In (1), a configuration ( a,b ) of two horizontal and vertical neighboring vertices is shown. In (2), a configuration ( a,b,c,d ) of a face is shown.
Source publication
Interaction-Round the Face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e., the models the Boltzmann weights of which satisfy the quantum Yang-Baxter equation, are of...
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Citations
... This paper is a continuation of the previous work [1]. Here, we present the Boltzmann weights (BWs) of the unrestricted Interaction-Round the Face (IRF) lattice model based on the affine Lie algebra su(3) k and the U q (sl(3)) quantum algebra, where the adjoint representation defines the admissibility conditions of the face configurations. ...
... It is well-established that certain lattice models at criticality are closely connected to two-dimensional conformal field theories 1 (CFTs). In our previous paper [1], we utilized this connection between CFT and restricted IRF models to determine the BWs for IRF models based on the affine Lie algebras su(2) k and su(3) k , considering various levels k and representations defining the admissibility conditions. We referred to that approach as the "CFT approach". ...
... In section 3, we discuss the Vertex-IRF correspondence and determine solutions for the BWs by finding the quantum R matrix and applying the mentioned correspondence. All the non-zero R matrix elements are listed in 1 Some examples include the Ising model [2], Yang-Lee edge singularity [3], the tricritical Ising model [4,5], the three-state Potts model [6,7], the eight-vertex SOS model [8,9], and IRF models based on affine Lie algebras [10][11][12]. 2 For instance, those properties conjectured in [13][14][15] regarding the fixed point theory of IRF models. ...
A bstract
This paper represents a continuation of our previous work, where the Boltzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically, the unrestricted face model, based on the su 3 k affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum R matrix of the U q sl 3 quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of R matrix elements.
... This paper is a continuation of the previous work [1]. Here, we present the Boltzmann weights (BWs) of the unrestricted Interaction-Round the Face (IRF) lattice model based on the affine Lie algebra su(3) k and the U q (sl(3)) quantum algebra, where the adjoint representation defines the admissibility conditions of the face configurations. ...
... It is well-established that certain lattice models at criticality are closely connected to two-dimensional conformal field theories 1 (CFTs). In our previous paper [1], we utilized this connection between CFT and restricted IRF models to determine the BWs for IRF models based on the affine Lie algebras su(2) k and su(3) k , considering various levels k and representations defining the admissibility conditions. We referred to that approach as the "CFT approach". ...
... The adjoint representation of the corresponding finite Lie algebra su(3) will be used to define the admissibility conditions for face configurations. A 1 Some examples include the Ising model [2], Yang-Lee edge singularity [3], the tricritical Ising model [4,5], the three-state Potts model [6,7], the eight-vertex SOS model [8,9], and IRF models based on affine Lie algebras [10][11][12]. 2 For instance, those properties conjectured in [13][14][15] regarding the fixed point theory of IRF models. ...
This paper represents a continuation of our previous work, where the Bolzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically the unrestricted face model, based on the affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum R matrix of the quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of R matrix elements.
