The value of the dynamic critical exponent z is studied for two-dimensional superconducting, superfluid, and Josephson Junction array systems in zero magnetic field via the Fisher-Fisher-Huse dynamic scaling. We find z ≃ 5.6 ± 0.3, a relatively large value indicative of non-diffusive dynamics. Universality of the scaling function is tested and confirmed for the thinnest samples. We discuss the validity of the dynamic scaling analysis as well as the previous studies of the Kosterlitz-Thouless-Berezinskii transition in these systems, the results of which seem to be consistent with simple diffusion (z = 2). Further studies are discussed and encouraged.

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We study the applicability of magnetization and specific heat equations derived from a lowest-Landau-level (LLL) calculation, to the high-temperature superconducting (HTSC) materials of the YBa2Cu3O 7−δ (YBCO) family. We find that significant information about these materials can be obtained from this analysis, even though the three-dimensional LLL functions are not quite as successful in describing them as the corresponding two-dimensional functions are in describing data for the more anisotropic HTSC Bi-and Tl-based materials. The results discussed include scaling fits, an alternative explanation for data claimed as evidence for a second order flux lattice melting transition, and reasons why 3DXY scaling may have less significance than previously believed. We also demonstrate how 3DXY scaling does not describe the specific heat data of YBCO samples in the critical region. Throughout the paper, the importance of checking the actual scaling functions, not merely scaling behavior, is stressed.

We have performed a renormalization-group analysis of a system of Kosterlitz-Thouless-Berezinskii (KTB) layers coupled to each other by a Lawrence-Doniach-type term, in zero field. We derive the recursion relations for the case where the interlayer coupling A, is weak. We find that A, is relevant and study the crossover away from KTB behavior. We have calculated the shift in the critical temperature and the size of the narrow three-dimensional critical region.