Condensed Matter Seminar: Ilya Gruzberg, OSU Department of Physics
Multifractals and conformal invariance
Event Details
- Date: Monday, March 30th, 2026
- Time: 10:00- 11:00 am
- Location: 1080 Physics Research Building
- Faculty Host: Mohit Randeria
Abstract
Multifractals are scale-invariant (critical) self-similar distributions of “stuff” that can be represented as clumpy irregular density profiles with a wide distribution of densities over the system. They arise in such diverse subjects as dynamical chaos, weather and climate, turbulence, fractal growth, critical clusters in statistical mechanics, disordered magnets, Anderson transitions and other random critical points, mathematical finance, random energy landscapes, Gaussian multiplicative chaos, and rigorous approaches to conformal field theory (CFT). A multifractal is characterized by a continuous spectrum of multifractal exponents Δ_q that describe the scaling of the moments of the underlying density with the system size. A field-theoretic description of multifractals is a long-standing challenge. Assuming that the field theories describing multifractals are CFTs, that is, the scale invariance is promoted to conformal invariance, we can use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum Δ_q must be quadratic in its arguments (parabolicity of the spectrum). We confront this finding with available numerical and analytical data for various Anderson transitions that unambiguously show clear deviations of the multifractal spectra Δ_q from parabolicity and discuss possible reasons for the discrepancy.
Bio
You can read more about Professor Gruzberg and his research on his profile page.