  I choose the Lee-Yang model and go through different approaches to analyze it
using the form factor approach and the bootstrap program, the lattice
description and the lattice TBA equations for a full understanding of the
model.
  The bootstrap program aims to explicitly solve 1+1 dimensional integrable
quantum field theories. In the first step, called the S-matrix bootstrap, the
scattering matrix, is determined from its properties. In developing a defect
form factor program the first step is the T-matrix bootstrap. Interacting
integrable defect theories are purely transmitting and topological. We analyze
both operators localized in the bulk and also on the defect. By finding their
solutions, the spectral representation of any correlator can be determined.
  Next we consider the model on the lattice. The lattice approach allows to
obtain both massive and massless excited TBA equations by studying the
continuum scaling limit of the associated integrable lattice models. The most
important input from the lattice approach is an insight into the analytic
structure of the excited state solutions of the TBA equations. Previously this
structure had to be guessed. In this thesis we turn our attention to the
simplest example of a non-unitary minimal theory, namely, the Lee-Yang minimal
model M(2,5). We study the Lee-Yang model on the lattice. We analyze the
periodic, boundary and the seam cases in both massive and massless regimes. We
derive their ground state TBA equations and analyze the flows between different
boundary and defect conditions.
  Finally, in the large volume limit, we calculate the L\"uscher correction
terms of the TBA energy of a one-particle state. We display those ideas in the
end of the thesis as this is an important direction of work in string theory,
particularly in the AdS/CFT correspondence.
