Harmonic measure of critical curves

E. Bettelheim; I. Rushkin; I. A. Gruzberg; P. Wiegmann

doi:10.1103/PhysRevLett.95.170602

Harmonic measure of critical curves

E. Bettelheim^*, I. Rushkin, I. A. Gruzberg, P. Wiegmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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 câ‰1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.1363] by relating the problem to boundary two-dimensional 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 câ‰1.

Original language	English
Article number	170602
Journal	Physical Review Letters
Volume	95
Issue number	17
DOIs	https://doi.org/10.1103/PhysRevLett.95.170602
State	Published - 21 Oct 2005
Externally published	Yes

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10.1103/PhysRevLett.95.170602

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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{\^a}‰1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.1363] by relating the problem to boundary two-dimensional 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{\^a}‰1.",

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N2 - 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 câ‰1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.1363] by relating the problem to boundary two-dimensional 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 câ‰1.

AB - 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 câ‰1, scaling exponents of the harmonic measure have been computed by Duplantier [Phys. Rev. Lett. 84, 1363 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.1363] by relating the problem to boundary two-dimensional 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 câ‰1.

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Harmonic measure of critical curves

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