Monte Carlo Simulation Of The Depinning Transi-tion In Low-dimensional Magnetic Models

Domain-wall dynamics is related to many important physical phenomena. The mo-tion of domain-wall has attracted much interest recently. The domain-wall motion occurs in ferroic materials, e.g., ferromagnetic materials and ferroelectric materials. The dynamics and the morphology of interface are depend on the strength and type of the driving force. And they vary with the temperature and the form of quenched randomness. The study of domain-wall is very important both in the theoretical and experimental fields. Theoreti-cally, the motion of domain-wall is a typical nonequilibrium dynamics. Experimentally, it is related to the new classes of storage instrument and the logic operation components. For the domain-wall motion in magnetic films, the Edwards-Wilkinson equation with quenched disorder (QEW) is a typical theoretical approach. The QEW equation is a phe-nomenological model, without detailed microscopic structures and interactions of materi-als. Furthermore, the theoretical self-inconsistence is puzzling in the QEW equation. In this dissertation, we focus on the dynamics of domain-wall in the low-dimensional magnetic film. Using Monte Carlo methods and short-time dynamics, we study the domain-wall dynamics of different lattice models, e.g., two-dimensional XY model, Ising model with quenched disorder and p-state clock model with quenched disorder. The two-dimensional XY model is discussed at Kosterlitz-Thouless (KT) transition temperature. Ising model and p-state clock model are discussed at zero temperature. Chapter2,3and4are the main results of our work.In Chapter1, we give a brief introduction to the dynamics of domain-wall. It includes the definition of domain wall, theoretical models, the morphology of magnetic domain wall and critical phenomena. The characteristic of ordered-disordered phase transition, KT phase transition and the universality class of the depinning transition are summarized. The main approaches are Monte Carlo method and the short-time dynamic approach. The mod- els include scalar model, continuous vector model and discrete vector model. Finally, we show the research motivation and the main research content.In Chapter2, we investigate the dynamic relaxation of a vortex state at the KT phase transition temperature of the two-dimensional XY model. A local pseudo-magnetization is introduced to describe the central symmetric structure of the dynamic systems. Based on the short-time dynamic approach, the dynamic scaling behavior of the pseudo-magnetization and Binder cumulant is carefully analyzed, and the critical exponents are determined. A strong logarithmic correction to scaling is detected in the core of the vortex state. The vor-tex density in the core even exceeds that of the disordered initial state. Therefore, it is not surprising that a strong logarithmic correction to scaling emerges. To illustrate the dynamic effect of the topological defect and the reliability of the defined pseudo-magnetization, sim-ilar analysis for the dynamic relaxation from a spin-wave state is also performed. We verify that a limited amount of quenched disorder in the core of the vortex state may alter the dy-namic universality class. Finally, theoretical calculations based on the linearized long-wave approximation are presented.In Chapter3, we systematically study the universality class of the depinning phase transition in the two-dimensional random-field Ising model with constant external field. We accurately locate the depinning transition field and determine both dynamic and static crit-ical exponents. The critical exponents vary significantly with the strength and form of the random fields. The strong universality of the depinning phase transition is violated. From the roughness exponents ζ,ζloc and ζs of domain-wall, one may judge that the depinning transition of the Ising model with quenched disorder belongs to a new dynamic universality class with ζ≠ζloc≠ζs and ζloc≠1. The crossover from the second-order transition to the first-order one is observed for the uniform distribution of the random fields which is bounded, but it is not present for the Gaussian distribution which is unbounded. The critical exponents exhibit independence from the updating schemes of the Monte Carlo algorithm. We verify that the random-single-spin-flip dynamics is robust. The DRFIM model does not suffer from the theoretical self-inconsistence as in the QEW equation, and its results are closer to experiments.In Chapter4, we investigate the short-time dynamic behavior of the depinning transi-tion in the two-dimensional p-state clock model for different random fields, with different constant driving fields respectively. The depinning transition field exhibits rather unusual dependence on the initial orientation. Unexpectedly, the dynamic effect of the random fields is the most significant for the domain interface with the smallest θR. We accurately determine the depinning transition field and both dynamic and static critical exponents. The results show that the critical exponents vary significantly with the initial orientation and both of the form and strength of the random fields. Similarly, the crossover from the first-order phase transition to the second-order one is obtained for the case of uniform dis-tribution of the random fields, but it is not present for the case of Gaussian distribution. For all cases, the roughness exponents ζ, ζloc and ζs are carefully obtained, and the results indicate that the depinning transition of the random-field p-state clock model belongs to the new dynamic universality class, which is the same as the random-field Ising model.In Chapter5, the main conclusions of this dissertation are summarized.