Random Defect Lines in Conformal Minimal Models

Abstract

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 ${\varphi }_{12}$ 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 $\eps \propto 1/m$ for the mth Virasoro minimal model. The decay exponents $X_N=\frac{N}{2}(1-\frac{9(3N-4)}{4(m+1{)}^2}+\mathcal{O}(\frac{3}{m+1}{)}^3)$ of the Nth moment of the two-point function of ${\varphi }_{12}$ along the defect are obtained to 2-loop order, exhibiting multifractal behavior.This leads to a typical decay exponent $X_{\mathrm{typ}}=1/2(1+\frac{9}{(m+1{)}^2}+\mathcal{O}(\frac{3}{m+1}{)}^3)$. 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/m^3. As a byproduct of our calculations, we also obtain to 2-loop order the exponent ${\tilde{X}}_N=N(1-\frac{2}{9{\pi }^2}(3N-4)(q-2{)}^2+\mathcal{O}(q-2{)}^3)$ of the Nth moment of the energy operator in the q-state Potts model with bulk bond disorder.

33 pages, 6 figures, LaTex

References in corpus (3)

• Multiscaling of energy correlations in the random-bond Potts model
• Correlated correlation functions in random-bond ferromagnets
• Further evidence of the absence of Replica Symmetry Breaking in Random Bond Potts Models

Cited by in corpus (5)

• TFT construction of RCFT correlators II: Unoriented world sheets
• On superuniversality in the $q$-state Potts model with quenched disorder
• Boundary conditions and defect lines in the Abelian sandpile model
• Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions