The vortex dynamics of a Ginzburg-Landau system under pinning effect

It is proved that the vortices are attracted by impurities or inhomogeities in the superconducting materials. The strong H^1-convergence for the corresponding Ginzburg-Landau system is also proved.Comment: 23page

Replica Monte Carlo Simulation (Revisited)

In 1986, Swendsen and Wang proposed a replica Monte Carlo algorithm for spin glasses [Phys. Rev. Lett. 57 (1986) 2607]. Two important ingredients are present, (1) the use of a collection of systems (replicas) at different of temperatures, but with the same random couplings, (2) defining and flipping clusters. Exchange of information between the systems is facilitated by fixing the tau spin (tau=sigma^1\sigma^2) and flipping the two neighboring systems simultaneously. In this talk, we discuss this algorithm and its relationship to replica exchange (also known as parallel tempering) and Houdayer's cluster algorithm for spin glasses. We review some of the early results obtained using this algorithm. We also present new results for the correlation times of replica Monte Carlo dynamics in two and three dimensions and compare them with replica exchange.Comment: For "Statistical Physics of Disordered Systems and Its Applications", 12-15 July 2004, Shonan Village Center, Hayama, Japan, 7 page