Two-dimensional quantum field theory obtained by perturbing the q-state Potts-model CFT (0<q<4) with the energy-density operator Φ(2, 1) is shown to be integrable. The particle content of this QFT is conjectured and the factorizable S matrix is proposed. The limit q→1 is related to the isotropic-percolation problem in 2D and so we make a few predictions about the size distributions of the percolating clusters in the scaling domain.

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.

In this paper we further elaborate on the notion of fractional exclusion statistics, as introduced by Haldane, in two-dimensional conformal field theory, and its connection to the Universal Chiral Partition Function as defined by McCoy and collaborators. We will argue that in general, besides the pseudo-particles introduced recently by Guruswamy and Schoutens, one needs additional 'null quasi-particles' to account for the null-states in the quasi-particle Fock space. We illustrate this in several examples of WZW-models.

We consider the massive tricritical Ising model M(4, 5) perturbed by the thermal operator ϕ 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r, s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m, n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r, s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.

We consider the massless tricritical Ising model M(4, 5) perturbed by the thermal operator ϕ 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r, s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m, n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandemonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.