Harmonic Measure of Critical Curves
Abstract
Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge c≤1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)PRLTAO0031900710.1103/PhysRevLett.84.1363] by relating the problem to boundary twodimensional gravity. We present a simple argument connecting the harmonic measure of critical curves to operators obtained by fusion of primary fields and compute characteristics of the fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with c≤1.
 Publication:

Physical Review Letters
 Pub Date:
 October 2005
 DOI:
 10.1103/PhysRevLett.95.170602
 arXiv:
 arXiv:hepth/0507115
 Bibcode:
 2005PhRvL..95q0602B
 Keywords:

 05.50.+q;
 05.45.Df;
 11.25.Hf;
 11.27.+d;
 Lattice theory and statistics;
 Fractals;
 Conformal field theory algebraic structures;
 Extended classical solutions;
 cosmic strings domain walls texture;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Some more corrections