Condensed Matter > Statistical Mechanics
[Submitted on 18 Jul 2012]
Title:Critical exponents in zero dimensions
View PDFAbstract:In the vicinity of the onset of an instability, we investigate the effect of colored multiplicative noise on the scaling of the moments of the unstable mode amplitude. We introduce a family of zero dimensional models for which we can calculate the exact value of the critical exponents $\beta_m$ for all the moments. The results are obtained through asymptotic expansions that use the distance to onset as a small parameter. The examined family displays a variety of behaviors of the critical exponents that includes anomalous exponents: exponents that differ from the deterministic (mean-field) prediction, and multiscaling: non-linear dependence of the exponents on the order of the moment.
Submission history
From: Alexandros Alexakis Dr [view email][v1] Wed, 18 Jul 2012 12:12:38 UTC (311 KB)
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