Universality of the off-equilibrium response function in the kinetic Ising chain

TL;DR

This paper demonstrates a universal relationship between off-equilibrium response and autocorrelation functions in a 1D Ising chain, independent of the spin-exchange or spin-flip dynamics, due to domain optimization effects.

Contribution

It reveals the universality of the response-correlation plot in 1D Ising chains and explains it through domain dynamics in a random environment.

Findings

The response-correlation plot is identical for different dynamics.

Universality arises from domain position optimization.

The mechanism is modeled with a single domain in a random environment.

Abstract

The off-equilibrium response function $\chi (t,t_w)$ and autocorrelation function $C(t,t_w)$ of an Ising chain with spin-exchange dynamics are studied numerically and compared with the same quantities in the case of spin-flip dynamics. It is found that, even though these quantities are separately different in the two cases, the parametric plot of $\chi (t,t_w)$ versus $C(t,t_w)$ is the same. While this result could be expected in higher dimensionality, where $\chi (C)$ is related to the equilibrium state, it is far from trivial in the one dimensional case where this relation does not hold. The origin of the universality of $\chi(C)$ is traced back to the optimization of domains position with respect to the perturbing external field. This mechanism is investigated resorting to models with a single domain moving in a random environment.