Spontaneous symmetry breaking in amnestically induced persistence

Details Spontaneous symmetry breaking in amnestically induced persistence Spontaneous symmetry breaking in amnestically induced persistence

2007-08-22

arxiv.org/abs/0708.3102v5

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 color figs

Scientific paper

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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