Scaling Limit of the Ising Model in a Field

Abstract

The dilute A_3 model is a solvable IRF (interaction round a face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of an Ising model at the critical temperature in a magnetic field. One therefore expects the scaling limit to be governed by Zamolodchikov's integrable perturbation of the c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz approach succeeded to unveil the corresponding E_8 structure under certain assumptions on the nature of the Bethe Ansatz solutions. In order to check these conjectures, we perform a detailed numerical investigation of the solutions of the Bethe Ansatz equations for the critical and off-critical model. Scaling functions for the ground-state corrections and for the lowest spectral gaps are obtained, which give very precise numerical results for the lowest mass ratios in the massive scaling limit. While these agree perfectly with the E_8 mass ratios, we observe one state which seems to violate the assumptions underlying the thermodynamic Bethe Ansatz calculation. We also analyze the critical spectrum of the dilute A_3 model, which exhibits massive excitations on top of the massless states of the Ising conformal field theory.

29 pages, RevTeX, 11 PostScript figures included by epsf, using amssymb.sty (v2.2)

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Cited by in corpus (14)

• Excited states in some simple perturbed conformal field theories
• Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field
• Short distance behaviour of correlators in the 2D Ising model in a magnetic field
• Magnetic Correlation Length and Universal Amplitude of the Lattice E_8 Ising Model
• Correction induced by irrelevant operators in the correlators 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
• The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
• Single Particle Excitations in the Lattice E_8 Ising Model
• Finite temperature corrections in 2d integrable models
• Universal amplitude ratios and Coxeter geometry in the dilute A model
• The inversion relation and the dilute A_{3,4,6} eigenspectrum
• The dilute A${}_4$ model, the E${}_7$ mass spectrum and the tricritical Ising model
• The dilute A_L models and the Phi_{1,2} perturbation of unitary minimal CFTs