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arXiv · 0708.3102

Spontaneous symmetry breaking in amnestically induced persistence

Marco Antonio Alves da Silva·A. S. Ferreira·G. M. Viswanathan·J. C. Cressoni
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Abstract

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.

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Marco Antonio Alves da Silva, A. S. Ferreira, G. M. Viswanathan, J. C. Cressoni. 2007-09-11. Spontaneous symmetry breaking in amnestically induced persistence. https://doi.org/10.1103/physreve.77.040101

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