Anomalous exponents at the onset of an instability

Abstract

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous, i.e. the mode amplitude X scales with departure from onset \mu as $<X> ~ \mu^\beta$ with an exponent $\beta$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability and our results provide a possible explanation to recent experimental observations.