Multifractality in spin glasses

Significance Many seemingly irregular objects (coast shores, for instance) look the same at different observation scales. In many cases, a single number, the fractal dimension, characterizes the scale changes. Other systems, known as multifractals, need a continuous range of parameters to characterize the change of scale. Multifractal behavior has been identified in a plethora of situations, from human heartbeats to financial time series, and is often accompanied by large statistical fluctuations. Spin glasses are one of the best-studied model systems for complexity, and large statistical fluctuations are completely absent from their dynamics. Our finding of multifractal scaling in the spin-glass off-equilibrium dynamics is, therefore, surprising. The paradox is solved through the concept of coherence length.