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We consider a one-dimensional classical ferromagnetic Ising model when it isquenched from a low temperature to zero temperature in finite time usingGlauber or Kawasaki dynamics. Most of the previous work on finite-time quenchesassume that the system is initially in equilibrium and focus on the excessdefect density at the end of the quench which decays algebraically in quenchtime with Kibble-Zurek exponent. Here we are interested in understanding theconditions under which the Kibble-Zurek scalings do not hold and in elucidatingthe full dynamics of the defect density. We find that depending on the initialconditions and quench time, the dynamics of the defect density can becharacterized by coarsening and/or the standard finite-time quench dynamicsinvolving adiabatic evolution and Kibble-Zurek dynamics; the time scales forcrossover between these dynamical phases are determined by coarsening time andstationary state relaxation time. As a consequence, the defect density at theend of the quench is either a constant or decays following coarsening laws orKibble-Zurek scaling. For the Glauber chain, we formulate a low temperaturescaling theory and find exact expressions for the final defect density forvarious initial conditions. For the Kawasaki chain where the dynamic exponentsfor coarsening and stationary state dynamics are different, we verify the abovefindings numerically and also examine the effect of unequal dynamic exponents.

Kibble-Zurek scalings and coarsening laws in slowly quenched classical Ising chains