Percolation and lack of self-averaging in a frustrated evolutionary model

Details Percolation and lack of self-averaging in a frustrated evolutionary model Percolation and lack of self-averaging in a frustrated evolutionary model

1998-06-22

arxiv.org/abs/cond-mat/9806259v1

Physics

Condensed Matter

Statistical Mechanics

22 pages, 1 figure

Scientific paper

We present a stochastic evolutionary model obtained through a perturbation of Kauffman's maximally rugged model, which is recovered as a special case. Our main results are: (i) existence of a percolation-like phase transition in the finite phase space case; (ii) existence of non self-averaging effects in the thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the space of all possible evolutions, analogous to that of a geometrically broken object. Thus the model turns out to be exactly solvable in the thermodynamic limit.

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