The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the Dynamical Cluster Approximation and Quantum Monte Carlo simulations as cluster solver. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.Despite years of active research, the understanding of pairing in the high-temperature "cuprate" superconductors (HTSC) remains one of the most important outstanding problems in condensed matter physics. While conventional superconductors are well described by the BCS theory, the pairing mechanism in HTSC is believed to be of entirely different nature. Strong electronic correlations play a crucial role in HTSC, not only for superconductivity but also for their unusual normal state behavior. Hence, models describing itinerant correlated electrons, in particular the two-dimensional (2D) Hubbard model and its strong-coupling limit, the 2D t-J model, were proposed to capture the essential physics of the CuO-planes in HTSC [1,2]. Despite the fact that these models are among the mostly studied models in condensed matter physics, the question of whether they contain enough ingredients to describe HTSC remains an unsolved problem.Many different techniques, from analytic to numerical have been applied to study superconductivity in these models. The Mermin-Wagner theorem [3] and the rigorous results in Ref.[4] preclude d x 2 −y 2 superconducting long-range order at finite temperatures in the 2D models. Superconductivity may however exist -as in the attractive Hubbard model -as topological order at finite temperatures below the Kosterlitz-Thouless (KT) transition temperature [5]. Recent renormalization group studies indicate that the ground-state of the doped weakcoupling 2D Hubbard model is superconducting with a d x 2 −y 2 -wave order parameter [6]. The possibility of d x 2 −y 2 -wave pairing in the 2D Hubbard and t-J models was also indicated in a number of numerical studies of finite system size (for a review see [7]). Only recent numerical calculations for the t-J model provided evidence for pairing at T = 0 in relatively large systems for physically relevant values of J/t [8]. Quantum Monte Carlo (QMC) simulations are also employed to search for such a transition [9]. These studies indicate an enhancement of the pairing correlations in the d x 2 −y 2 channel with decreasing temperature. Unfortunately the Fermion sign problem limits these studies to temperatures too high to study a possible KT transition. Another difficulty of these methods arises from their strong finite size effects, often ruling out the reliable extraction of low-energy scales. In fact, a reliable finite-size scaling has only recently been achieved in the negative-U model [10], where th...

Results are presented from experiments performed with the Community Climate System Model, version 4 (CCSM4) for the Coupled Model Intercomparison Project phase 5 (CMIP5). These include multiple ensemble members of twentieth-century climate with anthropogenic and natural forcings as well as single-forcing runs, sensitivity experiments with sulfate aerosol forcing, twenty-first-century representative concentration pathway (RCP) mitigation scenarios, and extensions for those scenarios beyond 2100–2300. Equilibrium climate sensitivity of CCSM4 is 3.20°C, and the transient climate response is 1.73°C. Global surface temperatures averaged for the last 20 years of the twenty-first century compared to the 1986–2005 reference period for six-member ensembles from CCSM4 are +0.85°, +1.64°, +2.09°, and +3.53°C for RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively. The ocean meridional overturning circulation (MOC) in the Atlantic, which weakens during the twentieth century in the model, nearly recovers to early twentieth-century values in RCP2.6, partially recovers in RCP4.5 and RCP6, and does not recover by 2100 in RCP8.5. Heat wave intensity is projected to increase almost everywhere in CCSM4 in a future warmer climate, with the magnitude of the increase proportional to the forcing. Precipitation intensity is also projected to increase, with dry days increasing in most subtropical areas. For future climate, there is almost no summer sea ice left in the Arctic in the high RCP8.5 scenario by 2100, but in the low RCP2.6 scenario there is substantial sea ice remaining in summer at the end of the century.

Supplementary data are available at Bioinformatics online.

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