Dynamic scaling at classical phase transitions approached through nonequilibrium quenching

作者：Liu Cheng Wei^*; Polkovnikov Anatoli; Sandvik Anders W

来源：Physical Review B, 2014, 89(5): 054307.

DOI：10.1103/PhysRevB.89.054307

We use Monte Carlo simulations to demonstrate generic scaling aspects of classical phase transitions approached through a quench (or annealing) protocol where the temperature changes as a function of time with velocity v. Using a generalized Kibble-Zurek ansatz, we demonstrate dynamic scaling for different types of stochastic dynamics (Metropolis, Swendsen-Wang, and Wolff) on Ising models in two and higher dimensions. We show that there are dual scaling functions governing the dynamic scaling, which together describe the scaling behavior in the entire velocity range v is an element of [0,infinity). These functions have asymptotics corresponding to the adiabatic and diabatic limits, and close to these limits they are perturbative in v and 1/v, respectively. Away from their perturbative domains, both functions cross over into the same universal power-law scaling form governed by the static and dynamic critical exponents (as well as an exponent characterizing the quench protocol). As a by-product of the scaling studies, we obtain high-precision estimates of the dynamic exponent z for the two-dimensional Ising model subject to the three variants of Monte Carlo dynamics: for single-spin Metropolis updates z(M) = 2.1767(5), for Swendsen-Wang multicluster updates z(SW) = 0.297(3), and for Wolff single-cluster updates z(W) = 0.30(2). For Wolff dynamics, we find an interesting behavior with a nonanalytic breakdown of the quasiadiabatic and diabatic scalings, instead of the generic smooth crossover described by a power law. We interpret this disconnect between the two scaling regimes as a dynamic phase transition of the Wolff algorithm, caused by an effective sudden loss of ergodicity at high velocity.

• 出版日期2014-2-24