Conformal invariance and surface defects in the two-dimensional Ising model. Exact results

The surface critical behavior of the two-dimensional Ising model with homogeneous perturbations in the surface interactions is studied on the one-dimensional quantum version. A transfer-matrix method leads to an eigenvalue equation for the excitation energies. The spectrum at the bulk critical point is obtained using anL^–1 expansion, whereL is the length of the Ising chain. It exhibits the towerlike structure which is characteristic of conformal models in the case of irrelevant surface perturbations (h_s/J_s0) as well as for the relevant perturbationh_s=0 for which the surface is ordered at the bulk critical point leading to an extraordinary surface transition. The exponents are deduced from the gap amplitudes and confirmed by exact finite-size scaling calculations. Both cases are finally related through a duality transformation.