Ye J, Machta J, Newman C M, Stein D L
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):040101. doi: 10.1103/PhysRevE.88.040101. Epub 2013 Oct 21.
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.
考虑一个具有随机初始状态的动力学多体系统，该系统随后通过随机动力学演化。在预测最终状态时，初始状态（“先天”）与随机动力学的实现（“后天”）的相对重要性是什么？我们针对二维伊辛铁磁体在从T = ∞ 到T = 0 的初始深度淬火之后的情况研究了这个问题。我们对在独立动力学环境中发展的“同卵双胞胎”之间的重叠进行了蒙特卡罗研究，系统规模最大达到L = 500。我们的结果表明，重叠随时间以t^(-θ)(h) 的形式衰减，其中θ(h) = 0.22 ± 0.02；对于淬火到低温但非零温度的情况，相同的指数也成立。这个“遗传指数”可能等于二维伊辛铁磁体的持久指数，但一般来说两者是不同的。
