Long-lived memory in sliding spin chains

We study a system of two ferromagnetic one-dimensional Ising chains coupled to a thermal bath, which are driven out of equilibrium by being moved past one another at a constant speed. We show that even at modest speeds, magnetic friction between the two chains significantly increases the ability of the system to order. In particular, at inverse temperature $\beta$, Ising coupling $J$, and sliding speed $v$, the dynamics retains memory of its initial magnetization for a time that increases from $\exp(O(\beta J))$ at $v = 0$ to $\exp(O((\beta J)^2v\ln v))$ when $v>v_c$, where $v_c$ is a small constant. Magnetic friction thus provides a simple mechanism for parametrically slowing down thermalization in a one-dimensional magnet.