Flux-lattice melting in two-dimensional disordered superconductors

The flux line lattice melting transition in two-dimensional pure and disordered superconductors is studied by a Monte Carlo simulation using the lowest Landau level approximation and quasi-periodic boundary condition on a plane. The position of the melting line was determined from the diffraction pattern of the superconducting order parameter. In the clean case we confirmed the results from earlier studies which show the existence of a quasi-long range ordered vortex lattice at low temperatures. Adding frozen disorder to the system the melting transition line is shifted to slightly lower fields. The correlations of the order parameter for translational long range order of the vortex positions seem to decay slightly faster than a power law (in agreement with the theory of Carpentier and Le Doussal) although a simple power law decay cannot be excluded. The corresponding positional glass correlation function decays as a power law establishing the existence of a quasi-long range ordered positional glass formed by the vortices. The correlation function characterizing a phase coherent vortex glass decays however exponentially ruling out the possible existence of a phase coherent vortex glass phase.Comment: 12 pages, 21 figures, final version to appear in Phys. Rev.

Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment

In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of quenched randomness, we introduce the idea of rare regions and discuss their importance. We then analyze in detail the different phenomena that can arise at magnetic quantum phase transitions in disordered metals, including quantum Griffiths singularities, smeared phase transitions, and cluster-glass formation. For each scenario, we discuss the resulting phase diagram and summarize the behavior of various observables. We then review several recent experiments that provide examples of these rare region phenomena. We conclude by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative Ising chain fixed, references added, v3: final version as publishe