No abstract

The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for P > ∼ 0.03.

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.

The frequency ω and temperature T dependent complex conductivity σ of two weakly coupled 2D XY models subject to the RSJ dynamics is studied through computer simulations. A double dissipation-peak structure in Re[ωσ] is found as a function of T for a fixed frequency. The characteristics of this double-peak structure, as well as its frequency dependence, is investigated with respect to the difference in the critical temperatures of the two XY models, originating from their different coupling strengths. The similarity with the experimental data in Festin et al. [Physica C 369, 295 (2002)] for a thin YBCO film is pointed out and some possible implications are suggested.

Recently, Kötzler et al.[1] measured the frequencydependent conductance for YBa 2 Cu 3 O 7 and interpreted their results as evidence that the decay of the superfluid density is caused by a 3D vortex-loop proliferation mechanism and a dimensional crossover when the correlation length c along the c axis becomes comparable to the sample thickness d. In this Comment, we show that the complex conductance data presented in Ref.[1] have characteristic key features not compatible with their analysis, which are instead described by the existing phenomenology of 2D vortex fluctuation in Ref.[2] associated with a partial decoupling of CuO 2 planes.In Fig. 1, G 0 in the complex conductance G G 0 iG 00 from Fig. 2 in Ref.[1] is replotted as !G 0 L k , with the kinetic inductance L k T extracted in Ref. [1]. In Ref.[1], it is assumed that !L k TG!; T S!=! 0 with a scaling function S S 0 iS 00 satisfying S 00 1=1 !=! 0 ÿ ;(1) and S 0 is obtained from the Kramer-Kronig relation [2]. Kötzler et al. find that their data can be characterized by 0:7, which corresponds to the heights of the dissipation peaks equal to 0.23 (solid line in Fig. 1). However, the data exceed this value by more than 40%, and the peak height shows a systematic increase with increasing frequency, whereas Eq. (1) predicts constant peak heights: Thus, the scaling function (1) cannot properly describe the experimental data. The 2D vortex explanation, on the other hand, predicts that the peak heights should systematically increase with ! and should always be between 1= 0:32 and 0.5 (dashed and dotted lines in the Fig. 1) [2,3]. The lower value 1= corresponds to the Minnhagen response form [given by 1 in Eq. (1)] associated with bound vortex-antivortex pairs dominating close to the Kosterlitz-Thouless (KT) transition. The higher value 1=2 corresponds to the Drude response [given by 2 in Eq. (1)], dominated by abundant free vortices well above the KT transition. Both free vortices and bound pairs are present above the KT transition with the proportion of free vortices increasing with T. This explains why the peak heights increase with T [2,3].Kötzler et al. link their proposed mechanism to an apparent sample independent onset of deviation at about 35 nH ÿ1 for the inductive data taken at 1 kHz from the inferred 3D L ÿ1 k . The KT criteria gives 7 nH ÿ1 which places the KT transition very close to the inferred 3D transition. Nevertheless, 35 and 7 are of the same order of magnitude, suggesting that the deviation at 1 kHz occurring below the inferred critical T c and the KT transition may indeed be caused by vortex loops. However, in such a scenario the deviation from the inferred zero frequency L ÿ1 k towards higher values is due to the finite frequency [2]. This deviation would then vanish in the limit of small frequency (small in the sense that the dissipation peaks in Fig. 1 cease to move to the left) implying a frequency dependent onset of deviations. Any change of the 3D L ÿ1 k caused by a dimensional crossover ( c * d) will always increase fluctuations and ca...