Comment on "Critical Dynamics of a Vortex-Loop Model for the Superconducting Transition"

Recently, Aji and Goldenfeldt [Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622] put forward an explanation for the value of the dynamic critical exponent z observed in certain Monte Carlo simulations of the superconducting phase transition in zero magnetic field. In this Comment, we point out that their analysis is based on incorrect assumptions regarding the scaling dimension of the vortex density.Comment: 1 page, no figure

Evidence of many thermodynamic states of the three-dimensional Ising spin glass

We present a large-scale simulation of the three-dimensional Ising spin glass with Gaussian disorder to low temperatures and large sizes using optimized population annealing Monte Carlo. Our primary focus is investigating the number of pure states regarding a controversial statistic, characterizing the fraction of centrally peaked disorder instances, of the overlap function order parameter. We observe that this statistic is subtly and sensitively influenced by the slight fluctuations of the integrated central weight of the disorder-averaged overlap function, making the asymptotic growth behaviour very difficult to identify. Modified statistics effectively reducing this correlation are studied and essentially monotonic growth trends are obtained. The effect of temperature is also studied, finding a larger growth rate at a higher temperature. Our state-of-the-art simulation and variance reduction data analysis suggest that the many pure state picture is most likely and coherent.Comment: 8 pages, 5 figure

Modeling and simulations of quantum phase slips in ultrathin superconducting wires

We study quantum phase slips (QPS) in ultrathin superconducting wires. Starting from an effective one-dimensional microscopic model, which includes electromagnetic fluctuations, we map the problem to a (1+1)-dimensional gas of interacting instantons. We introduce a method to calculate the tunneling amplitude of quantum phase slips directly from Monte Carlo simulations. This allows us to go beyond the dilute instanton gas approximation and study the problem without any limitations of the density of QPS. We find that the tunneling amplitude shows a characteristic scaling behavior near the superconductor-insulator transition. We also calculate the voltage-charge relation of the insulating state, which is the dual of the Josephson current-phase relation in ordinary superconducting weak links. This evolves from a sinusoidal form in the regime of dilute QPS to more exotic shapes for higher QPS densities, where interactions are important.Comment: 12 pages, 11 figure