Equilibrium And Dynamic Phase Transitions In Two-dimensional Frustrated Josephson Junction Arrays With Disorder

In this dissertation, using dynamic scaling theory, we have studied the equilibrium and dynamic phase transitions in two-dimensional frustrated Josephson junction arrays with disorder, which can be described by two-dimensional XY model. First, we have analyzed the superconducting phase transition, depinning transition at zero temperature and creeping laws at low temperatures when Josephson junction arrays are subjected to a weak magnetic field with the flux density 1/25. Then we have investigated the Ising-like phase transi-tion in weakly disordered Josephson junction arrays with the magnetic flux density 1/2. In the weak magnetic field, the random pinning potential is introduced into the coupling strength. Under the fluctuating twist boundary condition, the equilibrium superconduct-ing phase transition is discussed by means of dynamic scaling analysis of current-voltage characteristics. We also study the motion of vortices at zero temperature and creep at fi-nite temperatures by depinning and creeping scaling theory. The effects of disorder on the critical temperature, the critical current at zero temperature and the critical exponents are also discussed. As for the Josephson junction arrays in the strong magnetic field with the flux density 1/2, a random phase shift is added to the phase difference. Based on Monte Carlo simulations, the Ising-like phase transition is investigated in the short-time dynamic scaling scheme. The critical temperature, the static and dynamic critical exponents are also evaluated for different disorders. Finally, we have applied a short-time dynamic scaling method to the depinning phase transition of the quenched Mullins-Herring equation. For the first time we introduce a time-dependent Binder cumulant of the order parameter in the surface growth model and obtain the critical driving force and the critical exponents, which are consistent with those extracted from the long-time steady-state simulations.The main results of each part are as follows:(1) For the two-dimensional Josephson junction arrays exposed to the weak magnetic field with the flux density 1/25, the system undergoes a KTB phase transition in the ab- sence of disorder from a normal phase with linear resistivity to a superconducting state. When the disorder is introduced into the system, the phase transition would be driven into a non-KTB type, where a possible vortex glass transition is suggested by means of dynamic scaling analysis of current-voltage characteristics. It is found that the critical tem-perature increases with the disorder, but the dynamic exponent decreases. The values of static critical exponents are roughly the same within statistical errors, illustrating the same universality class in these continuous phase transitions with different disorder strengths. Whether the disorder is present or not, a continuous depinning transition is found at zero temperature and a non-Arrhenius creeping law is observed at low temperatures. The critical current changes nonmonotonously with the strength of the bond disorder. The depinning exponentβincreases and the thermal rounding exponent 8 decreases with the rise of dis-order. Interestingly, their product only has two characteristic values 2 and 5/3, depending on the strength of the disorder. These two characteristic values imply the existence of two universality classes in this model.(2) For the two-dimensional fully frustrated Josephson junction arrays in a strong magnetic field with the flux density 1/2, we first investigate the Ising-like phase transition in the system without disorder in a short-time dynamic method from two different initial states. It follows that the short-time dynamic scheme can be extended to such a disordered system, where the ground state is hard to obtain. Whereafter we have used this approach to study a possible Ising-like phase transition in the fully frustrated Josephson junction arrays with weak disorder. It is shown that the critical temperature decreases with disorder, and the static critical exponent increases, while the dynamic exponent varies slightly. More-over, there exists a critical disorder strengthσc above which the Ising-like phase transition disappears.(3) For the one-dimensional quenched Mullins-Herring surface growth model, the critical driving force and the critical exponents can be extracted by a short-time dynamic scaling approach. Compared with the long-time steady-state simulations, there exist two new points:(a). It is assumed that a universal dynamic scaling relation among the velocity, force and time is still valid in the macroscopic short-time regime. In this way, the time exponent 8 can be calculated in the short-time dynamic method; (b). In order to get the dynamic exponent independently, we introduce a time-dependent Binder cumulant of the order parameter growth velocity. Together with other scaling relations in this model, the present short-time dynamic approach can give equally good results as steady-state simula-tions. In addition, the finite size effects on the critical driving force and the exponents are also discussed. It is found that the finite size effects can well be controlled in the short-time dynamics, which highlights an advantage of this method.