Ubiquitous finite-size scaling features in I–V characteristics of various dynamic XY models in two dimensions

Abstract

Two-dimensional (2D) XY model subject to three different types of dynamics, namely Monte Carlo, resistivity shunted junction (RSJ), and relaxational dynamics, is numerically simulated. From the comparisons of the current-voltage (I-V ) characteristics, it is found that up to some constants I-V curves at a given temperature are identical to each other in a broad range of external currents. Simulations of the Villain model and the modified 2D XY model allowing stronger thermal vortex fluctuations are also performed with RSJ type of dynamics. The finite-size scaling suggested in Medvedyeva et al. [Phys. Rev. B (in press)] is confirmed for all dynamic models used, implying that this finite-size scaling behaviors in the vicinity of the Kosterlitz-Thouless transition are quite robust.

Dynamic scaling and two-dimensional high-Tcsuperconductors

“…We also find that the modified KTB scaling analysis is further weakened by its strong dependence on the voltage resolution limit of the experiment, as was theoretically demonstrated by Holzer et al 27 and in much the same way that the conventional vortex glass scaling is. 29 In distinction from modified KTB scaling, we find that a "ghost" transition based on the finite-size scaling of Medvedyeva et al 25,26 does not contain the same flexibility in determining the z. Despite this possible success of dynamic-scaling applied to a 2D superconductor, we find that the Medvedyeva et al finite-size scaling theory entails its own flexibility and we argue that the experimental data fall within this realm of flexibility.…”

“…This has important implications because it could easily account for the apparent universal result of z ≈ 6 that Pierson et al 17 and Ammirata et al 14 have determined on various systems, and in which there has been much recent interest. [24][25][26][27]32 These implications can be understood if we consider a comparison of several hypothetical measurements of the same sample made with varying sensitivities. If one would attempt to attribute a low universal value of z to all these measurements it would be found that the less sensitive ones would show good agreement with scaling (like those of Figs.…”

“…Later theoretical work by Colonna-Romano et al, 24 Medvedyeva et al, 25,26 and Holzer et al 27 suggests that the KTB transition can be obscured by finite-size effects. This work, in distinction from the earlier scaling analysis, 14,17 seems to support Repaci et al's original conclu-sions.…”

“…In addition, Medvedyeva et al 25,26 have proposed a finite-size scaling form that is also based on FFH-scaling applied to 2D superconductors. They argue that it is this finite-size scaling, as opposed to the modified KTB scaling, that is the correct scaling form for the data of Repaci et al They further argue that under certain conditions their finite-size scaling is of the same form as the modified KTB scaling analysis of Pierson and Ammirata.…”

Scaling determination of the nonlinearI−Vcharacteristics for two-dimensional superconducting networks

“…Ref. 19, MC dynamics gives for the same T the same I-V characteristics up to a constant factor and the same method as in Ref. 19 is used here.…”