Exact (d)->(+)&(-) boundary flow in the tricritical Ising model

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Abstract

The integrable perturbation of the degenerate boundary condition (d) by the \(\phi_{1,3}\) boundary field generates a renormalization group flow down to the superposition of Cardy boundary states (+)&(-). Exact Thermodynamic Bethe Ansatz (TBA) equations for all the excited states are derived here extending the results of a previous paper to this case. As an intermediate step, the non-Cardy boundary conformal sector (+)&(-) is also described as the scaling limit of an A_4 lattice model with appropriate integrable boundary conditions and produces the first example of superposition of finitized Virasoro characters.

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Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory

Subir Ghoshal, Alexander B Zamolodchikov (1993)

We study integrals of motion and factorizable S-matrices in two-dimensional integrable field theory with boundary. We propose the ``boundary cross-unitarity equation'' which is the boundary analog of the cross-symmetry condition of the ``bulk'' S-matrix. We derive the boundary S-matrices for the Ising field theory with boundary magnetic field and for the boundary sine-Gordon model.

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Boundary S-matrix for the Tricritical Ising Model

Leung Chim (1995)

The Tricritical Ising model perturbed by the subleading energy operator \Phi_(3/5) was known to be an Integrable Scattering Theory of massive kinks and in fact preserves supersymmetry. We consider here the model defined on the half-plane with a boundary and computed the associated factorizable boundary S-matrix. The conformal boundary conditions of this model were identified and the corresponding S-matrices were found. We also show how some of these S-matrices can be perturbed and generate ``flows'' between different boundary conditions.

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Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model

Ian Affleck (2000)

Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling constant. A boundary tri-critical point separates phases where the spins on the boundary are ordered or disordered. In the latter range of coupling constant, there is a non-zero critical field where the magnetization is singular. In the former range, as the temperature is lowered, the boundary undergoes a first order transition while the bulk simultaneously undergoes a second order transition.