Slow quenching for a one-dimensional kinetic Ising model: Residual energy and domain growth

Abstract

A one-dimensional kinetic Ising model with Glauber dynamics subjected to a slow continuous quench to zero temperature is studied. For a rather general class of cooling schemes, described by a time-dependent temperatureT(t), the mean domain sizeL(t) is calculated along with the residual energye _res (r) as a function of the cooling rater. If the attempt frequency α=α₀ exp(−ε/kT), entering into the transition rates, is temperature dependent (i.e., the barrier ε is non-zero), the asymptotic growth ofL(t) is given byL(∞)−L(t)~exp[−ε/kT(t)]. For this case the residual energy exhibits a power-law behaviore _res(r) ~r ^{δ/2(1 + δ)} forr small, where δ=4J/ε andJ is the nearest neighbor coupling constant. For ε=0 and for certain cooling schemes the residual energy is zero andL(t)~t1/2, independent ofr.