aqora

Critical phenomena at surfaces

Kurt Binder, David Paul Landau

Physica A Statistical Mechanics and its ApplicationsFeb 1, 199050 citations

On different approaches to integrable lattice models

Vladimir Belavin, Doron Gepner, J. Ramos Cabezas +1 more

Abstract 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 su ( 2 ) k and 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 su ( 3 ) k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R ^ matrix when the adjoint representation defines the admissibility conditions.Abstract 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 su ( 2 ) k and 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 su ( 3 ) k (for general k) and discuss how it can be used to find Boltzmann weights in terms of the quantum R ^ matrix when the adjoint representation defines the admissibility conditions.

arXiv:2308.10329Journal of Physics A Mathematical and TheoreticalMar 14, 20241 citation

IRF MODELS ASSOCIATED WITH REPRESENTATIONS OF THE LIE SUPERALGEBRAS gl (m|n) AND sl (m|n)

Tetsuo Deguchi, AKIRA FUJII

We present two families of exactly solvable interaction round a face (IRF) models associated with representation of the Lie superalgebras gl (m|n) and sl (m|n). These IRF models are the generalizations of integrable spin chains with bosons and fermions. We also presents fusion models associated with higher representation of gl (m|n) and sl (m|n). We introduce restricted IRF models both for gl (m|n) and sl (m|n).

Modern Physics Letters ADec 7, 19918 citations

Surface and finite size effects in critical phenomena

A. M. Nemirovsky, Karl F. Freed

Nuclear Physics BJan 1, 198622 citations

The effects of surfaces on dynamic critical behavior

S. Dietrich, Hans Werner Diehl

The European Physical Journal BDec 1, 198359 citations

On the free energy of solvable lattice models

Doron Gepner

We conjecture the inversion relations for thermalized solvable interaction round the face (IRF) two dimensional lattice models. We base ourselves on an ansatz for the Baxterization described in the 90's. We solve these inversion relations in the four main regimes of the models, to give the free energy of the models, in these regimes. We use the method of Baxter in the calculation of the free energy of the hard hexagon model. We believe these results to be quite general, shared by most of the known IRF models. Our results apply equally well to solvable vertex models. Using the expression for the free energy we calculate the critical exponent α, and from it the dimension of the perturbing (thermal) operator in the fixed point conformal field theory (CFT). We show that it matches either the coset O/G or G/O, where O is the original CFT used to define the model and G is some unknown CFT, depending on the regime. This agrees with known examples of such models by Huse and Jimbo et al.We conjecture the inversion relations for thermalized solvable interaction round the face (IRF) two dimensional lattice models. We base ourselves on an ansatz for the Baxterization described in the 90's. We solve these inversion relations in the four main regimes of the models, to give the free energy of the models, in these regimes. We use the method of Baxter in the calculation of the free energy of the hard hexagon model. We believe these results to be quite general, shared by most of the known IRF models. Our results apply equally well to solvable vertex models. Using the expression for the free energy we calculate the critical exponent α, and from it the dimension of the perturbing (thermal) operator in the fixed point conformal field theory (CFT). We show that it matches either the coset O/G or G/O, where O is the original CFT used to define the model and G is some unknown CFT, depending on the regime. This agrees with known examples of such models by Huse and Jimbo et al.

arXiv:2011.14108Nuclear Physics BSep 6, 20214 citations

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