Lattice Ising model in a field: E${}_8$ scattering theory

Abstract

Zamolodchikov found an integrable field theory related to the Lie algebra E${}_8$, which describes the scaling limit of the Ising model in a magnetic field. He conjectured that there also exist solvable lattice models based on E${}_8$ in the universality class of the Ising model in a field. The dilute A${}_3$ model is a solvable lattice model with a critical point in the Ising universality class. The parameter by which the model can be taken away from the critical point acts like a magnetic field by breaking the $\Integer_2$ symmetry between the states. The expected direct relation of the model with E${}_8$ has not been found hitherto. In this letter we study the thermodynamics of the dilute A${}_3$ model and show that in the scaling limit it exhibits an appropriate E${}_8$ structure, which naturally leads to the E${}_8$ scattering theory for massive excitations over the ground state.

11 pages, LaTeX

References in corpus (2)

• Order Parameters of the Dilute A Models
• Solvable lattice models labelled by Dynkin diagrams

Cited by in corpus (32)

• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Integrable field theory and critical phenomena. The Ising model in a magnetic field
• Angular quantization and form-factors in massive integrable models
• Differential equations and integrable models: the SU(3) case
• Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field
• Exceptional structure of the dilute A${}_3$ model: E${}_8$ and E${}_7$ Rogers--Ramanujan identities
• Short distance behaviour of correlators in the 2D Ising model in a magnetic field
• Scaling Limit of the Ising Model in a Field
• Fusion of Dilute $A_L$ Lattice Models
• Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
• Scaling and universality in the 2D Ising model with a magnetic field
• The perturbations ${\varphi }_{2,1}$ and ${\varphi }_{1,5}$ of the minimal models $M(p,p^{\prime })$ and the trinomial analogue of Bailey's lemma
• Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field
• Variational approach to the scaling function of the 2D Ising model in a magnetic field
• Correlation lengths and E_8 mass spectrum of the dilute A_3 lattice model
• Quantum Jacobi-Trudi Formula and $E_8$ Structure in the Ising Model in a Field
• Critical behaviour of the dilute O(n), Izergin-Korepin and dilute $A_L$ face models: Bulk properties
• Single Particle Excitations in the Lattice E_8 Ising Model
• The importance of being integrable: out of the paper, into the lab
• Excited State TBA for the ${\varphi }_{2,1}$ perturbed $M_{3,5}$ model
• Ising tricriticality and the dilute A${}_3$ model
• Surface operator content of the A_L face models
• From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curve
• Universal amplitude ratios and Coxeter geometry in the dilute A model
• Finite temperature corrections in 2d integrable models
• The inversion relation and the dilute A_{3,4,6} eigenspectrum
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• The Trigonometric $E_8$ R-matrix
• The dilute A${}_4$ model, the E${}_7$ mass spectrum and the tricritical Ising model
• The dilute A_L models and the integrable perturbations of unitary minimal CFTs
• The dilute A_L models and the Phi_{1,2} perturbation of unitary minimal CFTs