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arXiv:cond-mat/9609040 · Physical Review Letters

Monte Carlo Calculation of the Linear Resistance of a Three Dimensional Lattice superconductor Model in the London Limit

Hans Werner Weber, Henrik Jeldtoft Jensen

Published Mar 31, 1997• 26 citations
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Abstract

We have studied the linear resistance of a three dimensional lattice superconductor model in the London limit by Monte Carlo simulation of the vortex loop dynamics. We find excellent finite size scaling at the phase transition. We determine the dynamical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.51$ for the isotropic London lattice model.

DOI
10.1103/physrevlett.78.2620

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We have studied the linear resistance of a three dimensional lattice superconductor model in the London limit by Monte Carlo simulation of the vortex loop dynamics. We find excellent finite size scaling at the phase transition. We determine the dynamical exponent z=1.51z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.51z=1.51 for the isotropic London lattice model.
The anomalous dimension of the lattice London superconductor is determined from finite-size scaling of the susceptibility to be η ϕ = − 0.79(1). It is furthermore found that the vanishing of the vortex loop line tension in the 3D XY model, which should be related to that exponent, agrees reasonable well with this value of η ϕ . Deviations from this behavior are however also identified and it is suggested that they are an effect of the vortex loop intersections and therefore will vanish only in the limit of low vortex density.
We carry out Monte Carlo simulations of the three dimensional (3D) lattice London superconductor in zero applied magnetic field, making a detailed finite size scaling analysis of the Meissner transition. We find that the magnetic penetration length $\ensuremath{\lambda}$ and the correlation length $\ensuremath{\xi}$ scale as $\ensuremath{\lambda}\ensuremath{\sim}\ensuremath{\xi}\ensuremath{\sim}|t{|}^{\ensuremath{-}\ensuremath{\nu}}$, with $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.66\ifmmode\pm\else\textpm\fi{}0.03$, consistent with ordinary 3D XY\mathrm{XY}XY universality, ${\ensuremath{\nu}}_{\mathrm{XY}}\ensuremath{\approx}2/3$. Our results confirm the anomalous scaling dimension of magnetic field correlations at Tc{T}_{c}Tc​.
We investigate the critical behavior of the gauge-glass model for the vortex-glass transition in three-dimensional superconductors, including screening of the interaction between vortices. A Monte Carlo study of the linear resistivity and a scaling analysis of current-voltage characteristics indicates that screening destroys the finite-temperature transition found earlier when screening was neglected. The correlation-length exponent at the resulting zero-temperature transition is found to be $\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01$.
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.
We present a finite temperature Monte Carlo study of the XY\mathrm{XY}XY model in the vortex representation and study its dynamical critical behavior in two limits. The first neglects magnetic-field fluctuations, corresponding to the absence of screening, which should be a good approximation in high-Tc{T}_{c}Tc​ superconductors $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ except extremely close to the critical point. Here, from finite-size scaling of the linear resistivity we find the dynamical critical exponent of the vortex motion to be $z\ensuremath{\approx}1.5$. The second limit includes magnetic-field fluctuations in the strong screening limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}0)$ corresponding to the true asymptotic inverted XY\mathrm{XY}XY critical regime, where we find the unexpectedly large value $z\ensuremath{\approx}2.7.$ We compare these results, obtained from dissipative dynamics in the vortex representation, with the universality class of the corresponding model in the phase representation with propagating (spin-wave) modes. We also discuss the effect of disorder and the relevance of our results for experiments.
Monte Carlo simulations have been used to study a version of the XY model without vortex loops for J/T=0 on simple cubic and face-centered-cubic lattices. Finite-size scaling of data from L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L lattices with L up to 32 is used to obtain values for the order parameter \ensuremath{\Vert}M\ensuremath{\Vert} and a 1/L finite-size correction on each lattice. The order-parameter susceptibility is found to be diverging as L0.8{\mathit{L}}^{0.8}L0.8. We then study the crossover from three-dimensional to one-dimensional behavior on L\ifmmode\times\else\texttimes\fi{}W\ifmmode\times\else\texttimes\fi{}W simple cubic lattices, with W=4 and 8, and L up to 1024.