Two-Dimensional Copolymers and Exact Conformal Multifractality

Details Two-Dimensional Copolymers and Exact Conformal Multifractality Two-Dimensional Copolymers and Exact Conformal Multifractality

1998-12-31

arxiv.org/abs/cond-mat/9812439v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 1999

Scientific paper

10.1103/PhysRevLett.82.880

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.

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