1999/10/13 by Monwhea Jeng, Andreas W. W. Ludwig · 1 citation
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1016/s0550-3213(00)00639-8
published as Nucl. Phys. B 594 (2001) 685. · 33 pages, 6 figures, LaTex
arxiv created 1999/10/13 · arxiv updated 2009/11/30
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 \eps ∝ 1/m for the mth Virasoro minimal model. The decay exponents XN=(N)/(2)(1-(9(3N-4))/(4(m+1)2)+ O((3)/(m+1))3) 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 X\rm typ=1/2 (1+(9)/((m+1)2)+O((3)/(m+1))3). 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. As a byproduct of our calculations, we also obtain to 2-loop order the exponent XN=N(1-(2)/(9π2)(3N-4)(q-2)2+O(q-2)3) of the Nth moment of the energy operator in the q-state Potts model with bulk bond disorder.