Cooling dynamics of pure and random Ising chains

Abstract

The dynamics of the thermal quench for pure and random Ising chains is studied. Using theKibble–Zurek argument, we obtain for the pure Ising model that the density of kinks afterquenching decays as with the quench rate of temperature1/τ for largeτ. Forthe random Ising model, we show that the decay rates of the density of kinks and the residual energy are1/ln τ and1/(ln τ)2 respectivelyfor large τ. Analytic results for the random Ising model are confirmed by Monte Carlo simulation.Our results reveal a clear difference between classical and quantum quenches in the randomIsing chain.