We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ T c and the scaling region around the minimal model M 2,7 . For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian.

Using Watson's and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field φ(x) and the stress-energy tensor T µν (x) of Sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of T µν (x) to the sum rule of the c-theorem.

It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the form factor bootstrap approach. A sum rule which yields the scaling dimension of such operators is also derived.

The factorization condition for the scattering amplitudes of an integrable model with a line of defect gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal S-matrix in the bulk are only those with S = ±1. The choice S = −1 corresponds to the Ising model. We compute the transmission and reflection amplitudes relative to the interaction of the Majorana fermion with the defect and we discuss their relevant features.

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of inhomegeneity to the scattering amplitudes in the bulk. The factorization condition for the new amplitudes gives rise to a set of Reflection-Transmission equations. The solutions of these equations in the case of diagonal S-matrix in the bulk are only those with S = ±1. The choice S = −1 corresponds to the Ising model. We compute the exact expressions of the transmission and reflection amplitudes relative to the interaction of the Majorana fermion of the Ising model with the defect. These amplitudes present a weak-strong duality in the coupling constant, the self-dual points being the special values where the defect line acts as a reflecting surface. We also discuss the bosonic case S = 1 which presents instability properties and resonance states. Multi-defect systems which may give rise to a band structure are also considered. The exact expressions of correlation functions is obtained in terms of Form Factors of the bulk theory and matrix elements of the defect operator.

A non-perturbative method based on the Form Factor bootstrap approach is proposed for the analysis of correlation functions of 2-D massless integrable theories and applied to the massless flow between the Tricritical and the Critical Ising Models.

The one and two-particle form factors of the energy operator in the two-dimensional Ising model in a magnetic field at T = T c are exactly computed within the form factor bootstrap approach. Together with the matrix elements of the magnetisation operator already computed in ref. [7], they are used to write down the large distance expansion for the correlators of the two relevant fields of the model.The last years have seen important progresses in the non-perturbative study of twodimensional quantum field theories and related statistical mechanical models. If conformal symmetry provided us with an exact description of critical points and universality classes [1,2], the study of off-critical models turned out to be better approached within the framework of relativistic scattering theory. In fact, if the off-critical model under consideration is integrable (i.e. admits infinite conservation laws), it can be usually solved exploiting very general bootstrap techniques [3,4,5,6]. This circumstance appears to be particularly important in light of the fact that a large number of physically interesting two-dimensional systems can actually be described in terms of integrable models. A remarkable example is provided by the scaling limit of the two-dimensional Ising model in a magnetic field at T = T c (IMMF in the sequel) [4]. It can be formally described by the actionwhere A CF T denotes the action of the conformal minimal model M 3,4 and σ(x) the magnetisation operator of scaling dimension 2∆ σ = 1/8. The coupling constant h (magnetic field) has physical dimension h ∼ m 15/8 , m being a mass scale. Apart form the magnetisation operator, the only other relevant scaling field in the Ising model is the energy density ε(x) with scaling dimension 2∆ ε = 1.Zamolodchikov showed that the theory described by the action (1) possesses an infinite number of integrals of motion which can be used in order to determine the exact particle spectrum and S-matrix of the theory [4]. He found that the spectrum consists of eight massive particles A a (a = 1, 2, . . . , 8) whose masses stay in the following ratios with the mass m 1 of the lightest particle The interaction between these particles is described by a factorised, reflectionless S-matrix 1 characterised by the two-particle amplitudesThe set of numbers A ab and the multiplicity factors µ α are given in Table 1. We use the standard rapidity parameterisation of the on-shell momenta pIn ref.[7] the knowledge of the S-matrix (3) was exploited in order to approach the computation of the correlation functions of the model (1) within the form factor bootstrap method. The basic idea of this approach is to express the (euclidean) correlation functions (e.g. the two-point ones) as a spectral sum over a complete set of intermediate multiparticle statesand to exploit the fact that the form factors (FF)are exactly computable in integrable models once the S-matrix is known [8,6]. The spectral series (4) is manifestly a large distance expansion. Nevertheless, it has been observed in several...

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $\Phi_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models.Comment: 13pgs, harvmac, 2 fig