Nature vs. Nurture: Predictability in Low-Temperature Ising Dynamics

TL;DR

This study investigates the predictability of the final state in a 2D Ising ferromagnet after a quench, revealing a heritability exponent that characterizes the influence of initial conditions versus stochastic dynamics.

Contribution

It introduces the concept of a heritability exponent in Ising dynamics and provides numerical estimates, linking initial state influence to persistence properties.

Findings

Overlap decays as t^(-0.22) with time

Heritability exponent may equal the persistence exponent

Results hold for quenches to zero and low nonzero temperatures

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") vs. 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 $T=\infty$ 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 $t^{-\theta_h}$ with $\theta_h = 0.22 \pm 0.02$; the same exponent holds for a quench to low but nonzero temperature. This "heritability exponent" may equal the persistence exponent for the 2D Ising ferromagnet, but the two differ more generally.