We thoroughly revisit the ferromagnetic Ising chain under Glauber dynamics in the case where temperature depends on time according to an arbitrary protocol. We show how the Glauber theory simplifies in the low-temperature scaling regime where the typical size of the ferromagnetic domains is much larger than the lattice spacing. We analyse in depth various classes of protocols, including slow quenches over a large but finite quenching time, everlasting slow quenches, periodic temperature protocols, and the Kovacs effect. The key observables are the density of domain walls, the susceptibility, and their dimensionless product referred to as the form factor. Our quantitative results are compared to the phenomenological Kibble-Zurek scaling theory whenever such a comparison is possible. Based on a recent work in collaboration with Claude Godrèche.

IPhT