Random defect lines in conformal minimal models Original Research Article

We analyze the effect of adding quenched disorder along a defect line in the 2D conformal minimal models using replicas. The disorder is realized by a random applied magnetic field in the Ising model, by fluctuations in the ferromagnetic bond coupling in the tricritical Ising model and tricritical three-state Potts model (the φ12 operator), etc. We find that for the Ising model, the defect renormalizes to two decoupled half-planes without disorder, but that for all other models, the defect renormalizes to a disorder-dominated fixed point. Its critical properties are studied with an expansion in ϵ∝1/m for the mth Virasoro minimal model. The decay exponents XN=N21−9(3N−4)4(m+1)2+O3m+13 of the Nth moment of the two-point function of φ12 along the defect are obtained to 2-loop order, exhibiting multifractal behavior. This leads to a typical decay exponent Xtyp=121+9(m+1)2+O3m+13. One-point functions are seen to have a non-self-averaging amplitude. The boundary entropy is larger than that of the pure system by order 1/m3.