Corrections to scaling in two-dimensional dynamic XY and fully frustrated XY models

Spin-reorientation critical dynamics in the two-dimensional XY model with a domain wall

In recent years, static and dynamic properties of non-180^{∘} domain walls in magnetic materials have attracted a great deal of interest. In this paper, spin-reorientation critical dynamics in the two-dimensional XY model is investigated with Monte Carlo simulations and theoretical analyses based on the Langevin equation. At the Kosterlitz-Thouless phase transition, the dynamic scaling behaviors of the magnetization and the two-time correlation function are carefully analyzed, and critical exponents are accurately determined. When the initial value of the angle between adjacent domains is slightly lower than π, a critical exponent is introduced to characterize the abnormal power-law increase of the magnetization in the horizontal direction inside the domain interface, which is measured to be ψ=0.0568(8). In addition, the relation ψ=η/2z is analytically deduced from the Langevin dynamics in the long-wavelength approximation, well consistent with numerical results.

Numerical simulations of critical dynamics in anisotropic magnetic films with the stochastic Landau-Lifshitz-Gilbert equation

With the stochastic Landau-Lifshitz-Gilbert (sLLG) equation, critical dynamic behaviors far from equilibrium or stationary around the order-disorder and pinning-depinning phase transitions in anisotropic magnetic films are investigated. From the dynamic relaxation with and without an external field, the Curie temperature and critical exponents of the order-disorder phase transition are accurately determined. For the pinning-depinning phase transition induced by quenched disorder, the nonstationary creep motion of domain wall activated by finite temperatures is simulated, and the thermal rounding exponent is extracted. The results show that the dynamic universality class of the sLLG equation is different from those of the Monte Carlo dynamics and quenched Edwards-Wilkinson equation, and it may lead to alternative understanding of experiments. The dynamic approach shows its great efficiency for the sLLG equation.

Critical domain-wall dynamics of model B

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .

Logarithmic correction to scaling in domain-wall dynamics at Kosterlitz-Thouless phase transitions

With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional XY model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.

Short-time critical dynamics at perfect and imperfect surfaces

With Monte Carlo simulations, we study the dynamic relaxation at perfect and imperfect surfaces of the three-dimensional Ising model with an ordered initial state. The time evolution of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and second cumulants is carefully examined. Universal dynamic scaling forms including a dynamic crossover scaling form are identified at the ordinary, special, and surface phase transitions. The critical exponents beta1 of the surface magnetization and beta2 of the line magnetization are extracted. The impact of the defect line on the universality classes is investigated.

Nonequilibrium critical dynamics with domain wall and surface

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.

Short-time critical dynamics and aging phenomena in the two-dimensional XY model

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.

Short-time dynamics of a family of XY noncollinear magnets

Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that XY antiferromagnetic systems undergo a (weak) first-order phase transition accompanied by pseudocritical scaling.

Continuous majority-vote model

We introduce a kinetic irreversible XY model and investigate its dynamic critical behavior through short-time Monte Carlo simulations on square lattices with periodic boundary conditions, starting from an ordered state. We find evidence that this system exhibits a Kosterlitz-Thouless-like phase for low values of the noise parameter. We present results for the correlation function exponent eta for several noise values. We also find that the dynamic critical exponent z is in agreement with the value expected for local update Monte Carlo rules.