Critical Interfaces in the Random-Bond Potts Model
Abstract
We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin-Kasteleyn (FK) domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We also obtain numerical results for the fractal dimension of spin clusters interfaces for q=3. These are found numerically consistent with the duality κspinκFK=16 as expressed in putative SLE parameters.
- Publication:
-
Physical Review Letters
- Pub Date:
- February 2009
- DOI:
- 10.1103/PhysRevLett.102.070601
- arXiv:
- arXiv:0809.3985
- Bibcode:
- 2009PhRvL.102g0601J
- Keywords:
-
- 05.50.+q;
- 75.60.Ch;
- Lattice theory and statistics;
- Domain walls and domain structure;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 4 pages