Monte Carlo calculation of the current-voltage characteristics of a two-dimensional lattice Coulomb gas

Weber, Hans; Wallin, Mats

doi:10.1103/physrevb.53.8566

Cited by 33 publications

(30 citation statements)

References 26 publications

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“…7 for the mapping between two models), where the same values of the dynamic critical exponent (z = z scale = 1/ǫT CG − 2) have been found in MC dynamics. 46 Also, the continuum CG model with Langevin dynamics of the pure relaxational form has been found to give the same values of z.…”

Section: 14mentioning

confidence: 74%

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

2000

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The dynamic critical exponent z is determined numerically for the d-dimensional 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 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.

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Section: 14mentioning

confidence: 74%

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

2000

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“…4, J s has been indirectly measured via the I-V characteristics in the nonohmic regime ͓see discussion above Eq. ͑28͔͒, given within the KT theory by 13,17,35 …”

Section: Role Of Inhomogeneitiesmentioning

confidence: 99%

Broadening of the Berezinskii-Kosterlitz-Thouless superconducting transition by inhomogeneity and finite-size effects

2009

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We discuss the crucial role played by finite-size effects and inhomogeneity on the Berezinskii-KosterlitzThouless ͑BKT͒ transition in two-dimensional superconductors. In particular, we focus on the temperature dependence of the resistivity, that is dominated by superconducting fluctuations above the BKT transition temperature T BKT and by inhomogeneity below it. By means of a renormalization-group approach we establish a direct correspondence between the parameter values used to describe the BKT fluctuation regime and the distance between T BKT and the mean-field Ginzburg-Landau transition temperature. Below T BKT a resistive tail arises due to finite-size effects and inhomogeneity, that reflects also on the temperature dependence of the superfluid density. We apply our results to recent experimental data in superconducting LaAlO 3 / SrTiO 3 heterostructures, and we extract several informations on the microscopic properties of the system from our BKT fitting parameters. Finally, we compare our approach to recent data analysis presented in the literature, where the physical meaning of the parameter values in the BKT formulas has been often overlooked.

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“…Applications involving such surface interactions include the study of planar circuits in electrical engineering, a variety of problems in thin films [5,19,20], and certain problems in tomography [7]. In quasi-geostrophic fluid dynamic models [17], one encounters an equation analogous to the incompressible Navier-Stokes equations which take the form…”

Section: Introductionmentioning

confidence: 99%

Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian

Gimbutas¹,

Greengard²,

Minion³

2001

SIAM J. Sci. Comput.

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We present an adaptive fast multipole method for inverting the square root of the Laplacian in two dimensions. Solving this problem is the dominant computational cost in many applications arising in electrical engineering, geophysical fluid dynamics, and the study of thin films. It corresponds to the evaluation of the field induced by a planar distribution of charge or vorticity. Our algorithm is direct and assumes only that the source distribution is discretized using an adaptive quad-tree. The amount of work grows linearly with the number of mesh points.

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Monte Carlo calculation of the current-voltage characteristics of a two-dimensional lattice Coulomb gas

Cited by 33 publications

References 26 publications

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

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

Broadening of the Berezinskii-Kosterlitz-Thouless superconducting transition by inhomogeneity and finite-size effects

Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian

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