Cooling dynamics of pure and random Ising chains

TL;DR

This paper investigates the cooling dynamics of pure and random Ising chains, revealing different decay behaviors of kink density and residual energy during temperature quenches, supported by analytical and simulation results.

Contribution

It provides new analytical and numerical insights into the non-equilibrium dynamics of pure and random Ising chains during temperature quenches.

Findings

Kink density decays as 1/√τ in pure Ising chains.

In random Ising chains, decay rates are 1/lnτ for kink density and 1/(lnτ)^2 for residual energy.

Monte-Carlo simulations confirm the analytical predictions.

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/\sqrt{\tau} with the quench rate of temperature 1/\tau for large \tau. For the random Ising model, we show that decay rates of the density of kinks and the residual energy are 1/\ln\tau and 1/(\ln\tau)^2 for large \tau respectively. 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.