Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9912325 · Europhysics Letters (EPL)

Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids

L. M Jensen, B. J Kim, Petter Minnhagen

Published Mar 1, 2000• 14 citations
arXivHTMLPDF

Abstract

The dynamic critical exponent z is determined from numerical simulations for the three-dimensional XY model subject to two types of dynamics, i.e. , relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well as for two different treatments of the boundary, i.e. , periodic boundary condition (PBC) and fluctuating twist boundary condition (FTBC). In case of relaxational dynamics, finite-size scaling at the critical temperature gives z ≈ 2 for PBC and 1.5 for FTBC, while for RSJ dynamics z ≈ 1.5 is obtained in both cases. The results are discussed in the context of superfluid/superconductors and vortex dynamics, and are compared with what has been found for other related models.

DOI
10.1209/epl/i2000-00199-0

Related papers

Dynamic critical exponent of two-, three-, and four-dimensional XY models with relaxational and resistively shunted junction dynamics

Lars Melwyn Jensen, Beom Jun Kim, Petter Minnhagen

The dynamic critical exponent z is determined numerically for the d-dimensional $\mathrm{XY}$ model $(d=2,$ 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: $z=2,$ 3/2, and 2 for $d=2,$ 3, and 4, respectively.

arXiv:cond-mat/0003447•Physical review. B, Condensed matter•Jun 1, 2000•44 citations

Short-Time Resistively-Shunted Junction Dynamic Study on Two-Dimensional Fully Frustrated XY Model

Y.-K. Yu, Meng‐Bo Luo, Ying He-Ping +1 more

Short-time dynamic behaviour of two-dimensional fully frustrated XY model near the Ising-like phase-transition temperature is studied with resistively shunted junction dynamics. The transition temperature T c and the dynamic and static critical exponents z , 2β/ν and ν are estimated under both a periodic boundary condition (PBC) and a fluctuating twist boundary condition (FTBC) using the short-time dynamic scaling analysis. The results show that T c , 2β/ν and ν are almost independent of the boundary conditions, whereas z depends on the boundary condition. The value of z = 2.18(5) of the PBC is roughly equal to that of the FF XY model with Monte Carlo dynamics under the PBC, while z = 2.05(4) of the FTBC is in agreement with that of the Coulomb gas model.

Chinese Physics Letters•Dec 1, 2003•2 citations

Vortex dynamics for two-dimensional XY models

Beom Jun Kim, Petter Minnhagen, Peter Olsson

Two-dimensional $\mathrm{XY}$ models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent z in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature ${T}^{\mathrm{CG}}$ and the vortex renormalization given by the dielectric constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}) z=1/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}{T}^{\mathrm{CG}}\ensuremath{-}2>~2$ both for RSJ and TDGL and that the nonlinear $\mathrm{IV}$ exponent a is given by $a=z+1$ in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.

arXiv:cond-mat/9806231•Physical review. B, Condensed matter•May 1, 1999•54 citations

Analysis of current-voltage characteristics of two-dimensional superconductors: Finite-size scaling behavior in the vicinity of the Kosterlitz-Thouless transition

Kateryna Medvedyeva, Beom Jun Kim, Petter Minnhagen

It has been suggested [Pierson et al., Phys. Rev. B 60, 1309 (1999); Ammirata et al., Physica C 313, 225 (1999)] that for two-dimensional (2D) superconductors there exists a phase transition with the dynamic critical exponent $z\ensuremath{\approx}5.6.$ We perform simulations for the 2D resistively-shunted-junction model and compare the results with the experimental data in Repaci et al. obtained for an ultrathin YBCO sample [Phys. Rev. B 54, R9674 (1996)]. We then use a different method of analyzing dynamic scaling than in Pierson et al., and conclude that both the simulations and the experiments are consistent with a conventional Kosterlitz Thouless (KT) transition in the thermodynamic limit for which $z=2.$ For finite systems, however, we find both in simulations and experiments that the change in the current-voltage $(I\ensuremath{-}V)$ characteristics caused by the finite size shows a scaling property with an exponent $\ensuremath{\alpha}\ensuremath{\approx}1/6,$ seemingly suggesting a vanishing resistance at a temperature for which $z={\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is pointed out that the dynamic critical exponent found in Pierson et al. corresponds to the exponent ${\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is emphasized that this scaling property does not represent any true phase transition since in reality the resistance vanishes only at zero temperature. Nevertheless, the observed scaling behavior associated with $\ensuremath{\alpha}\ensuremath{\approx}1/6$ appears to be a common and intriguing feature for the finite size caused change in the $I\ensuremath{-}V$ characteristics around the KT transition.

arXiv:cond-mat/0009291•Physical review. B, Condensed matter•Dec 1, 2000•41 citations

Current-voltage characteristics of the two-dimensional XY model with Monte Carlo dynamics

Beom Jun Kim

Current-voltage characteristics and the linear resistance of the two-dimensional $\mathrm{XY}$ model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent z at various temperatures. From the comparison with the resistively shunted junction dynamics, it is concluded that z is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.

arXiv:cond-mat/0010121•Physical review. B, Condensed matter•Dec 13, 2000•10 citations

Vortex Glass Transition in a Random Pinning Model

Anders Vestergren, Jack Lidmar, Mats Wallin

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.

arXiv:cond-mat/0111216•Physical Review Letters•Mar 5, 2002•24 citations
The dynamic critical exponent z is determined from numerical simulations for the three-dimensional XY model subject to two types of dynamics, i.e. , relaxational dynamics and resistively shunted junction (RSJ) dynamics, as well as for two different treatments of the boundary, i.e. , periodic boundary condition (PBC) and fluctuating twist boundary condition (FTBC). In case of relaxational dynamics, finite-size scaling at the critical temperature gives z ≈ 2 for PBC and 1.5 for FTBC, while for RSJ dynamics z ≈ 1.5 is obtained in both cases. The results are discussed in the context of superfluid/superconductors and vortex dynamics, and are compared with what has been found for other related models.
The dynamic critical exponent z is determined numerically for the d-dimensional XY\mathrm{XY}XY model (d=2,(d=2,(d=2, 3, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of z are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the same boundary condition do not always give the same value of z. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of z consistent with expectations for superfluids and superconductors: z=2,z=2,z=2, 3/2, and 2 for d=2,d=2,d=2, 3, and 4, respectively.
Short-time dynamic behaviour of two-dimensional fully frustrated XY model near the Ising-like phase-transition temperature is studied with resistively shunted junction dynamics. The transition temperature T c and the dynamic and static critical exponents z , 2β/ν and ν are estimated under both a periodic boundary condition (PBC) and a fluctuating twist boundary condition (FTBC) using the short-time dynamic scaling analysis. The results show that T c , 2β/ν and ν are almost independent of the boundary conditions, whereas z depends on the boundary condition. The value of z = 2.18(5) of the PBC is roughly equal to that of the FF XY model with Monte Carlo dynamics under the PBC, while z = 2.05(4) of the FTBC is in agreement with that of the Coulomb gas model.
Two-dimensional XY\mathrm{XY}XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent z in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature TCG{T}^{\mathrm{CG}}TCG and the vortex renormalization given by the dielectric constant $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}) z=1/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}{T}^{\mathrm{CG}}\ensuremath{-}2>~2$ both for RSJ and TDGL and that the nonlinear IV\mathrm{IV}IV exponent a is given by a=z+1a=z+1a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.
It has been suggested [Pierson et al., Phys. Rev. B 60, 1309 (1999); Ammirata et al., Physica C 313, 225 (1999)] that for two-dimensional (2D) superconductors there exists a phase transition with the dynamic critical exponent $z\ensuremath{\approx}5.6.$ We perform simulations for the 2D resistively-shunted-junction model and compare the results with the experimental data in Repaci et al. obtained for an ultrathin YBCO sample [Phys. Rev. B 54, R9674 (1996)]. We then use a different method of analyzing dynamic scaling than in Pierson et al., and conclude that both the simulations and the experiments are consistent with a conventional Kosterlitz Thouless (KT) transition in the thermodynamic limit for which z=2.z=2.z=2. For finite systems, however, we find both in simulations and experiments that the change in the current-voltage $(I\ensuremath{-}V)$ characteristics caused by the finite size shows a scaling property with an exponent $\ensuremath{\alpha}\ensuremath{\approx}1/6,$ seemingly suggesting a vanishing resistance at a temperature for which $z={\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is pointed out that the dynamic critical exponent found in Pierson et al. corresponds to the exponent ${\ensuremath{\alpha}}^{\ensuremath{-}1}.$ It is emphasized that this scaling property does not represent any true phase transition since in reality the resistance vanishes only at zero temperature. Nevertheless, the observed scaling behavior associated with $\ensuremath{\alpha}\ensuremath{\approx}1/6$ appears to be a common and intriguing feature for the finite size caused change in the $I\ensuremath{-}V$ characteristics around the KT transition.
Current-voltage characteristics and the linear resistance of the two-dimensional XY\mathrm{XY}XY model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent z at various temperatures. From the comparison with the resistively shunted junction dynamics, it is concluded that z is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.
We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.