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

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 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.