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arXiv:cond-mat/9605087 · Physical review. B, Condensed matter

Monte Carlo study of a three-dimensional vortex-glass model with screening

Carsten Wengel, A. P. Young

Published Sep 1, 1996• 33 citations
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Abstract

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 $\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01$.

DOI
10.1103/physrevb.54.r6869

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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 \ensuremathν=1.05\ifmmode±\else\textpm\fi0.01\ensuremath{\nu}=1.05\ifmmode\pm\else\textpm\fi{}0.01\ensuremathν=1.05\ifmmode±\else\textpm\fi0.01.
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.
The scaling behavior of the current-voltage characteristics of chiral and gauge-glass models of disordered superconductors, are studied numerically, in two dimensions. For both models, the linear resistance is nonzero at finite temperatures and the scaling analysis of the nonlinear resistivity is consistent with a phase transition at T=0T=0T=0 temperature characterized by a diverging correlation length $\ensuremath{\xi}\ensuremath{\propto}{T}^{\ensuremath{-}{\ensuremath{\nu}}_{T}}$ and thermal critical exponent ${\ensuremath{\nu}}_{T}.$ The values of ${\ensuremath{\nu}}_{T},$ however, are found to be different for the chiral and gauge-glass models, suggesting different universality classes, in contrast to the result obtained recently in three dimensions.
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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.
We have studied the three-dimensional Ising spin glass with a $\ifmmode\pm\else\textpm\fi{}J$ distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite-size scaling analysis shows quite strong evidence for a finite transition temperature Tc{T}_{c}Tc​ with ordering below Tc{T}_{c}Tc​. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent $\ensuremath{\nu}$ is somewhat higher. Because there may be (unknown) corrections to finite-size scaling, we do not completely rule out the possibility that Tc=0{T}_{c}=0Tc​=0 or that Tc{T}_{c}Tc​ is finite but with no order below Tc{T}_{c}Tc​. However, from our data, these possibilities seem less likely.