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arXiv:hep-th/9108024 · International Journal of Modern Physics A

ON THE S MATRIX OF THE SUBLEADING MAGNETIC DEFORMATION OF THE TRICRITICAL ISING MODEL IN TWO DIMENSIONS

Filippo Colomo, Giuseppe Mussardo, A. KOUBEK

Published Aug 20, 1992• 29 citations
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Abstract

We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.

DOI
10.1142/s0217751x92002416

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International Journal of Modern Physics A•Oct 20, 1991•156 citations
We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.
The tricritical Ising model perturbed by the subleading energy operator [Formula: see text] was known to be an integrable scattering theory of massive kinks,14 and in fact it preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and compute the associated factorizable boundary S matrix. The conformal boundary conditions of this model are identified and the corresponding S matrices are found. We also show how some of these S matrices can be perturbed and generate “flows” between different boundary conditions.
We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator phi2,1\\phi_{2,1}phi2,1​. This operator has conformal dimensions (7/16,7/16)(7/16,7/16)(7/16,7/16) and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.
A (1+1)-dimensional quantum field theory with a degenerate vacuum (in finite volume) can contain particles, known as kinks, which interpolate between different vacua and have non-trivial restrictions on their multi-particle Hilbert space. Assuming such a theory to be integrable, we show how to calculate the multi-kink energy levels in finite volume given its factorizable S-matrix. In massive theories this can be done exactly up to contributions due to off-shell and tunneling effects that fall off exponentially with volume. As a first application we compare our analytical predictions for the kink scattering theories conjectured to describe the sub-leading thermal and magnetic perturbations of the tricritical Ising model with numerical results from the truncated conformal space approach. In particular, for the sub-leading magnetic perturbation our results allow us to decide between the two different S-matrices proposed by Smirnov and Zamolodchikov.
The critical Ising model perturbed by the spin field (conjugated to the magnetic field) is studied numerically by the method of truncated fermionic space of states. The matrix elements of the perturbed Hamiltonian are found between the states of free Majorana fermions living on a finite-length circle. The Hamiltonian spectrum is studied numerically in the level-5 truncated space. Reasonable estimations are obtained for the vacuum energy, a part of the mass spectrum and the simplest scattering amplitude of the perturbed system.