New solvable lattice models from conformal field theory

Baver, Ernest

doi:10.1016/0370-2693(96)01090-8

Cited by 3 publications

(8 citation statements)

References 18 publications

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“…The main examples for such models are WZW theories, see, e.g., [8,9,15]. Other models based on other CFT's are known in the literature, see [17], but for the most part these models remain to be explored explicitly in the future.…”

Section: Discussionmentioning

confidence: 99%

The crossing multiplier for solvable lattice models

2022

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We study the large class of solvable lattice models, based on the data of conformal ﬁeld theory. These models are constructed from any conformal ﬁeld theory. We consider the lattice models based on aﬃne algebras described by Jimbo et al., for the algebras ABCD and by Kuniba et al. for G2. We ﬁnd a general formula for the crossing multipliers of these models. It is shown that these crossing multipliers are also given by the principally specialized characters of the model in question. Therefore we conjecture that the crossing multipliers in this large class of solvable interaction round the face lattice models are given by the characters of the conformal ﬁeld theory on which they are based. We use this result to study the local state probabilities of these models and show that they are given by the branching rule, in regime III.

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Section: Discussionmentioning

confidence: 99%

The crossing multiplier for solvable lattice models

2022

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“…In section 5, we summarize our results and briefly discuss possible applications to a class of IRF models based on a quotient SU(n) k Zn [21]. The case n = 2 has already been studied in [22]. For n > 2, the problem of multiplicity arises, and we expect that the present research results will help find exact solutions for this class of IRF models.…”

Section: Introductionmentioning

confidence: 85%

“…where a * represents the conjugate representation of a, this allows us to reduce the set of unknowns, see [22]. The results of these computations are presented in the subsequent subsections.…”

Section: Cft Approachmentioning

confidence: 99%

On different approaches to integrable lattice models

Belavin,

Gepner,

Ramos Cabezas

et al. 2024

J. Phys. A: Math. Theor.

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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 particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras $\mathfrak{su}(2)_k$ and $\mathfrak{su}(3)_k$ are computed for fundamental and adjoint representations for some fixed levels $k$. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on $\mathfrak {su}(3)_k$ (for general $k$) and discuss how it can be used to find Boltzmann weights in terms of the quantum $\hat{R}$ matrix when the adjoint representation defines the admissibility conditions.

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“…, 𝑛 − 2. Thus, if the crossing multipliers of the model are given by the character (14), and (16) holds, then, one can give arguments to conjecture that (see [10] for the details of these arguments), in the regime III of the model which is defined by 0 < 𝑞 < 1 and 0 < 𝑢 < 𝑙 and in the limit 𝑞 ′ → 0, (𝑞 ′ ) 𝑢 → 𝑓 𝑖𝑥𝑒𝑑, the LSP is given by…”

Section: Local State Probabilitymentioning

confidence: 99%

“…The main examples for such models are WZW theories, see, [5,6]. Other models based on other CFTs (coset of affine Lie algebras) are known in the literature, see [14]. However, for the most part, these models remain to be explored explicitly in the future.…”

Section: Pos(ichep2022)432mentioning

confidence: 99%

A large family of IRF solvable lattice models based on WZW models

Belavin¹,

Gepner²

2022

Proceedings of 41st International Conference on High Energy Physics — PoS(ICHEP2022)

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We consider the lattice models based on affine algebras described by Jimbo et al., for the algebras 𝐴𝐵𝐶𝐷 and by Kuniba et al. for 𝐺 2 . We find a general formula for the crossing multipliers of these models, with the result that these crossing multipliers are given by the principally specialized characters of the model in question. Therefore we conjecture that the crossing multipliers in a large class of solvable interaction round the face lattice models are given by the characters of the conformal field theory on which they are based. We also elaborate on some details of the computation of the Local state probability of these models, conjecturing an expression for it.

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New solvable lattice models from conformal field theory

Cited by 3 publications

References 18 publications

The crossing multiplier for solvable lattice models

The crossing multiplier for solvable lattice models

On different approaches to integrable lattice models

A large family of IRF solvable lattice models based on WZW models

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