Conformally invariant fractals and potential theory

被引：124

作者：

Duplantier, B ^{[1
]}

机构：

[1] Serv Phys Theor Saclay, F-91191 Gif Sur Yvette, France

[2] Inst Henri Poincare, F-75231 Paris 05, France

[3] Isaac Newton Inst Math Sci, Cambridge CB3 0HE, England

来源：

PHYSICAL REVIEW LETTERS | 2000年 / 84卷 / 07期

关键词：

D O I：

10.1103/PhysRevLett.84.1363

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension (f) over cap(theta) of the boundary set with local wedge angle theta is (f) over cap(theta) = pi/theta - 25-c/12 (pi-theta)(2)/theta(2 pi-theta), with c the central charge of the model. As a corollary, the dimensions D-EP of the external perimeter and D-H of the hull of a Potts cluster obey the duality equation (D-EP - 1)(D-H - 1) = 1/4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.

引用

页码：1363 / 1367

页数：5

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