### Abstract

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state ("nature") versus the realization of the stochastic dynamics ("nurture") in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from T=∞ to T=0. We performed Monte Carlo studies on the overlap between "identical twins" raised in independent dynamical environments, up to size L=500. Our results suggest an overlap decaying with time as t^{-}θ_{h} with θ_{h}=0.22±0. 02; the same exponent holds for a quench to low but nonzero temperature. This "heritability exponent" may equal the persistence exponent for the two-dimensional Ising ferromagnet, but the two differ more generally.

Original language | English (US) |
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Article number | 040101 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 88 |

Issue number | 4 |

DOIs | |

State | Published - Oct 21 2013 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*88*(4), [040101]. https://doi.org/10.1103/PhysRevE.88.040101