Dynamic scaling at classical phase transitions approached through nonequilibrium quenching
Abstract
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 KibbleZurek ansatz, we demonstrate dynamic scaling for different types of stochastic dynamics (Metropolis, SwendsenWang, 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 ∈[0,∞). 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 powerlaw scaling form governed by the static and dynamic critical exponents (as well as an exponent characterizing the quench protocol). As a byproduct of the scaling studies, we obtain highprecision estimates of the dynamic exponent z for the twodimensional Ising model subject to the three variants of Monte Carlo dynamics: for singlespin Metropolis updates z_{M}=2.1767(5), for SwendsenWang multicluster updates z_{SW}=0.297(3), and for Wolff singlecluster 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.
 Publication:

Physical Review B
 Pub Date:
 February 2014
 DOI:
 10.1103/PhysRevB.89.054307
 arXiv:
 arXiv:1310.6327
 Bibcode:
 2014PhRvB..89e4307L
 Keywords:

 64.60.De;
 64.60.F;
 64.60.Ht;
 05.70.Ln;
 Statistical mechanics of model systems;
 Equilibrium properties near critical points critical exponents;
 Dynamic critical phenomena;
 Nonequilibrium and irreversible thermodynamics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 18 figures