Critical properties of an altered Ising model

A modified two-dimensional Ising model is studied. In this model the nearest-neighbor interactions are changed along an infinite line imbedded in the lattice. We show that the effect of this alteration can be represented by the action of a marginal operator on the critical Ising model. This marginal operator is seen to change the decays of correlation in the lattices near the altered line. We find that the magnetization index is changed, while the index remains fixed. The expected crossover of the correlation functions to bulk behavior is also observed. We calculate the critical index for the disorder variable and predict the following relation between the index for the order and disorder variables: 2x_{}+2x_{}=1.