二維Ginzburg-Landau模型模擬第二類超導的熱擾動和無序現象

Abstract

在本論文中，我們使用二維金斯堡-朗道模型及準動量基底來模擬二維第二類超導體，並由蒙地卡羅方法來分析研究其在熱擾動和無序影響下的行為。在有序條件下，我們計算了漩渦系統的Abrikosov ratio、比熱、內能、漩渦的排列情況及結構係數。由於內能的分布圖呈現雙峰的結構，我們判斷系統的相變屬於弱一級相變，並且推論無限大系統的相變約化溫度 t_m~ -14.1。藉由分析Bragg peaks在動量空間的行為，可以得知分別在液態和固態條件下漩渦的詳細排列狀況。我們測量了結構係數和溫度及系統尺寸的關係圖，分別得到了各系統的漩渦晶格熔點以及結構係數與溫度的代數關係。接著，對系統加入了一個隨機亂數場，使系統變成了無序的狀態。然後討論了有序和無序系統在漩渦排列和結構函數的差異處，並且更進一步的分析無序系統的磁化率來試著得到漩渦液態和玻璃態的分界線。

The thermal fluctuations and disorder in two dimensional Ginzburg-Landau model in the quasimomentum basis are studied by Monte Carlo simulation. In the pure vortex system, the Abrikosov ratio, specific heat, internal energy and structure factor were calculated. The melting phase transition is weakly first order as is inferred from a double - peak of the internal energy distribution. The melting reduced (dimensionless) temperature t_m~ -14.1 is extrapolated for the infinite system size. The behavior of Bragg peaks indicates that the different of arrangement of solid and liquid states. The temperature and size dependence of structure factor shows the melting temperature t_m of flux-line-lattice and the algebraic relation of system size and structure factor. The 〖δT〗_c disorder is simulated by adding the random potential field is added to the quadratic term of the GL energy. The difference between the pure and the disordered system is demonstrated by snapshots of the vortex configurations and the structure factor. I tried to locate the glass line of disorder system by analyzing the distribution of magnetization.