Pre-freezing of multifractal exponents in random energy models with a logarithmically correlated potential
Abstract
Boltzmann-Gibbs measures generated from logarithmically correlated random potentials are multifractal. We investigate the abrupt change ('pre-freezing') of multifractality exponents extracted from the averaged moments of the measure—the so-called inverse participation ratios. The pre-freezing can be identified with termination of the disorder-averaged multifractality spectrum. The naive replica limit employed to study a one-dimensional variant of the model is shown to break down at the pre-freezing point. Further insights are possible when employing zero-dimensional and infinite-dimensional versions of the problem. In particular, the latter version allows one to identify the pattern of the replica symmetry breaking responsible for the pre-freezing phenomenon.
- Publication:
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Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- July 2009
- DOI:
- 10.1088/1742-5468/2009/07/P07022
- arXiv:
- arXiv:0903.2502
- Bibcode:
- 2009JSMTE..07..022F
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- This is published version, 11 pages, 1 figure