Conformal invariance and linear defects in the two-dimensional Ising model

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Using conformal invariance, we show that the non-universal exponent eta₀ associated with the decay of correlations along a defect line of modified bonds in the square-lattice Ising model is related to the amplitude A₀=xiₙ/n of the correlation length ξₙ(Kc) at the bulk critical coupling Kc, on a strip with width n, periodic boundary conditions and two equidistant defect lines along the strip, through A₀=(πη₀)⁻¹.