Cooling dynamics of pure and random Ising chains

Abstract

Dynamics of quenching temperature is studied in pure and random Ising chains. Using the Kibble-Zurek argument, we obtain for the pure Ising model that the density of kinks after quenching decays as 1/\sqrtτ with the quench rate of temperature 1/τfor large τ. For the random Ising model, we show that decay rates of the density of kinks and the residual energy are 1/\lnτand 1/(\lnτ)^2 for large τrespectively. Analytic results for the random Ising model are confirmed by the Monte-Carlo simulation. Our results reveal a clear difference between classical and quantum quenches in the random Ising chain.

10 pages and 2 figures, published version