Kramers-Wannier Dualities via Symmetries

Ruelle, Philippe

doi:10.1103/physrevlett.95.225701

Cited by 10 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first systematic study of logarithmic CFT appeared in [21]. Logarithmic CFTs are currently the subject of intensive investigation, see [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] and references therein. There is of course a long history of studying percolation as the continuum scaling limit of lattice models [40,41,42].…”

Section: Introductionmentioning

confidence: 99%

Fusion algebra of critical percolation

2007

View full text Add to dashboard Cite

We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite direct sum of these representations. The fusion rules are commutative, associative and exhibit an sℓ(2) structure. They involve representations which we call Kac representations of which some are reducible yet indecomposable representations of rank 1. In particular, the identity of the fusion algebra is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the recent results of Eberle-Flohr and Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of indecomposable representations of rank 3. Our fusion rules are supported by extensive numerical studies of an integrable lattice model of critical percolation. Details of our lattice findings and numerical results will be presented elsewhere.

show abstract

Section: Introductionmentioning

confidence: 99%

Fusion algebra of critical percolation

2007

View full text Add to dashboard Cite

show abstract

“…[52,54]). For very large values of η, the natural counterpart of the E 7 theory for the TIM is the thermal perturbation of the IM described in Section 2: both theories are self-dual and have a Z 2 symmetric action 8 .…”

Section: Stability Of the E 7 Action And The Flow To The Ising Modelmentioning

confidence: 99%

“…Dualities of the Kramers-Wannier type are extremely useful in understanding universality classes and phase diagrams of a model. In the special case of two-dimensional critical phenomena, invariant under general symmetries (such as translation, rotation and dilation transformations) and with universal properties described by conformal field theories [4,5], it has been shown that the information about duality is encoded in the fusion algebra of special fields associated with conformal defects [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model

Cubero,

Konik,

Lencsés

et al. 2021

Preprint

View full text Add to dashboard Cite

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E 7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, σ(x) and σ (x), in either phase are accompanied by associated disorder operators, µ(x) and µ (x). Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For σ(x) and σ (x), the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest Z 2 odd particles. Similarly, the equations for µ(x) and µ (x) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for σ(x)/σ (x) are fixed in terms of those for µ(x)/µ (x). We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the ∆-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

show abstract

Section: Introductionmentioning

confidence: 99%

Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

et al. 2022

View full text Add to dashboard Cite

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E_7E7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, \sigma(x)σ(x) and \sigma'(x)σ′(x), in either phase are accompanied by associated disorder operators, \mu(x)μ(x) and \mu'(x)μ′(x). Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For \sigma(x)σ(x) and \sigma'(x)σ′(x), the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest \mathbb{Z}_2ℤ2 odd particles. Similarly, the equations for \mu(x)μ(x) and \mu'(x)μ′(x) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for \sigma(x)/\sigma'(x)σ(x)/σ′(x) are fixed in terms of those for \mu(x)/\mu'(x)μ(x)/μ′(x). We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the \DeltaΔ-sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

show abstract

Kramers-Wannier Dualities via Symmetries

Cited by 10 publications

References 18 publications

Fusion algebra of critical percolation

Fusion algebra of critical percolation

Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model

Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

Contact Info

Product

Resources

About