Non-equilibrium critical dynamics with domain interface

Abstract

With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface.In the past years, much effort of physicists has been devoted to the understanding of nonequilibrium dynamic processes. Phase ordering dynamics, spin glass dynamics, structural glass dynamics and interface growth etc are important examples. Since the pioneer work by Janssen et al [1], the universal dynamic scaling form in critical dynamics has been explored up to the macroscopic short-time regime [1-10], when the system is still far from equilibrium.Although the spatial correlation length is still short in the beginning of the time evolution, the short-time dynamic scaling form is induced by the divergent correlating time around a continuous phase transition. Based on the short-time dynamic scaling form, new methods for the determination of both dynamic and static critical exponents as well as the critical temperature have been developed [4,5,[7][8][9][10][11]. Since the measurements are carried out in the short-time regime, one does not suffer from critical slowing down.In understanding the dynamic scaling form far from equilibrium, we should keep in mind that it holds after a time scale t mic , which is sufficiently long in the microscopic sense, but still short in the macroscopic sense. More importantly, the macroscopic initial condition should be taken into account in the dynamic scaling form [1,9,12]. For the dynamic relaxation starting from an ordered state, i.e., a state with an initial magnetization m 0 = 1, for example, the magnetization decays by a power law [8,9,12]. If m 0 is smaller but close to 1, there emerge corrections to scaling. For the dynamic relaxation starting from a random state, i.e., a state without spatial correlations and with a small m 0 , however, the magnetization does not decay, and rather shows an initial increase in the macroscopic short-time regime. An independent critical exponent x 0 must be introduced to describe the scaling dimension of the initial magnetization [1,6,9,10]. If m 0 = 0, the magnetization naturally remains zero during the dynamic evolution, but x 0 is still needed to describe the auto-correlation function etc. This critical exponent also explains the power-law decay of the remanent magnetization in spin glasses [2,13,14]. On the other hand, the short-time dynamic scaling form is universal, in the sense that it does not depend on the microscopic details of the dynamic system, such as the lattice types, interactions, and updating schemes etc. Up to now, the dynamic relaxation with the ordered and random initial states has been systematically investigated.Recent progress in the non-equilibrium critical dynamics and its applications includes, for

Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States

“…1. We find that similar to the classical case, [22,23] as the time evolves, the sharp domain wall will blur and expand into an interfacial region. Let us focus on the behavior of the local parameter at the position 𝑥, with 𝑥 denoting the distance to the initial domain wall.…”

“…[21] In particular, critical relaxation dynamics with a domain interface in a semi-ordered initial state was studied. [22,23] Those works showed that different from the relaxation dynamics with a homogeneous initial state, the initial domain wall can expand into a growing interfacial region, and in this region the order parameter decays obeying a distinct scaling relation 𝑀 ∝ 𝑡 −𝛽 1 /𝜈𝑧 with 𝛽1 being an additional dynamic exponent. In quantum sys-tems, exotic prethermal dynamics induced by the interface in the 2D quantum Ising model was discovered.…”

Nonsteady dynamic properties of a domain wall for the creep state under an alternating driving field

“…As time evolves, the domain wall moves and roughens, while the bulk remains unchanged. Therefore, the domain wall can also be called a domain interface [46,47]. Main results of numerical simulations are presented with the lattice size L x = 25 and L y = 512, up to t max = 400 000 Monte Carlo steps (MCS).…”

Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets

“…Recent activities include various applications and developments such as theoretical and numerical studies of the Josephson junction arrays and aging phenomena [45][46][47][48][49]. A kind of domain-wall roughening process at order-disorder phase transitions has also been revealed [50][51][52]. Very recently, the short-time behavior of the domain-wall relaxation around the depinning transition is noted in simulations and experiments [14,15,53].…”