MARGINAL EXTENDED PERTURBATIONS IN 2 DIMENSIONS AND GAP EXPONENT RELATIONS

The most general form of a marginal extended perturbation in a two-dim ensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surfac e, a line or a point for which exact results have been previously obta ined. The first-order corrections to the local exponents, which are fu nctions of the amplitude of the defect, are deduced from a perturbatio n expansion of the two-point correlation functions. Assuming covarianc e under conformal transformation, the perturbed system is mapped onto a cylinder. Working in the Hamiltonian limit, the first-order correcti ons to the lowest gaps are calculated for the Ising model. The results confirm the validity of the gap-exponent relations for the perturbed system.