Critical curves in conformally invariant statistical systems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


We consider critical curves-conformally invariant curves-that appear at critical points of two-dimensional statistical mechanical systems. We showhow to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.

Original languageAmerican English
Pages (from-to)2165-2195
Number of pages31
JournalJournal of Physics A: Mathematical and Theoretical
Issue number9
StatePublished - 2 Mar 2007
Externally publishedYes


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