Theoretical Study Of Phase Transitions In Superconducting System

Phase transition occurs in many aspects of superconductivity. In this Ph. D. thesis, several phase transitions in superconducting systems are studiedWe numerically investigate the intriguing effects produced by random per-colative disorder in two-dimensional Josephson-junction arrays. By dynam-ic scaling analysis, we evaluate critical temperatures and critical exponents with high accuracy. It is observed that, with the introduction of site-diluted disorder, the Kosterlitz-Thouless-Berezinsky(KTB) phase transition is elim-inated and evolves into a continuous transition with power-law divergent correlation length. Moreover, genuine depinning transition and creep mo-tion are studied, evidence for distinct creep motion types is provided. Our results not only are in good agreement with the recent experimental find-ings, but also shed some light on the relevant phase transitions. We also investigate the finite-temperature phase transition in another typ-ical diluted Josephson junction arrays—bond-diluted Josephson junction arrays. The phase transitions are shown to be non-KTB type. However, we do not observe any evidence of the combined phase transition which is present in site-diluted Josephson junction arrays.We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region (J< 0)—a model for high-Tc cuprate. In the J→-∞limit, we map the AT model onto a fully-packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion of AT model, we develop a variant of worm algorithm, which significantly suppress the critical slowing-down. We analyze the Monte Carlo data by finite-size scal-ing, and locate a line of critical points belong to the Ising universality class in the region J<0 and K>0, with K the four-spin interaction. Further, we find that, as J→-∞, the critical line terminates at the decoupled point K= 0.From our numerical results, we conjecture that the ending point (J→-∞, K=0) is KTB-like. Near this point, the dynamic exponent of the newly developed worm algorithm is estimated as z=0.25(1).Large-scale simulations have been performed on the current-driven two-dimensional XY gauge glass model (a model for glassy phase in High-Tc superconductor) with resistively-shunted-junction dynamics. It is observed that the linear resistivity at low temperatures tends to zero, providing strong evidence of glass transition at finite temperature. Dynamic scal-ing analysis demonstrates that perfect collapses of current-voltage data can be achieved with the glass transition temperature Tg=0.22, the corre-lation length critical exponent v=1.8, and the dynamic critical exponent z=2.0. A genuine continuous depinning transition is found at zero temper-ature. For creeping at low temperatures, critical exponents are evaluated and a non-Arrhenius creep motion is observed in the glass phase.We perform a first-principle study on the flux-lattice melting in the novel iron-based superconductor LaOo.9Fo.1FeAs and LaOo.925Fo.o75FeAs. Using the Hypernetted-Chain closure and an efficient algorithm, we calculate the two-dimensional one-component plasma pair distribution functions, static structure factors and direct correlation functions at various temperatures. The Hansen-Verlet freezing criterion is shown to be valid for vortex-liquid freezing in type-Ⅱsuperconductors. Finally, flux-lattice melting lines for LaOo.9Fo.1FeAs and LaOo.925Fo.o75FeAs are predicted through the combina-tion of the density functional theory and the mean-field substrate approach. This is the first theoretical study of vortex matter in the iron-based super-conductor.We explore the emerging ordered phases in hardcore bosonic mixture on a triangular optical lattice, using worm-type worldline Quantum Monte Carlo method. We observe a clear evidence for the existence of supersolid and super-counter fluid states. The critical behavior is analyzed by finite-size scaling scheme. Moreover, a supersolid-supersolid state is observed. By large-scale simulations, we finally obtain the phase diagram of hardcore bosonic mixture on the triangular optical lattice.We not only develop some numerical methods in the study of various phase transitions in superconducting system, but also characterize their universality class with the numerical evidence, from various perspectives.