Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model

Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general confirmation of finite-size scaling in non-equilibrium dynamics, this allows to test the scaling behaviour of the plateau height $C_{\infty}^{(2)}$ to which the two-time auto-correlator converges, when deep into the finite-size regime.