arXiv:cond-mat/9710200 · Physical Review Letters

Critical Behavior of the Meissner Transition in the Lattice London Superconductor

Peter Olsson, Stephen Teitel

Published Mar 2, 1998• 53 citations

Abstract

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 $\mathrm{XY}$ universality, ${\ensuremath{\nu}}_{\mathrm{XY}}\ensuremath{\approx}2/3$. Our results confirm the anomalous scaling dimension of magnetic field correlations at ${T}_{c}$.

DOI: 10.1103/physrevlett.80.1964

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arXiv:cond-mat/9710200 · Physical Review Letters

Critical Behavior of the Meissner Transition in the Lattice London Superconductor

Peter Olsson, Stephen Teitel

Published Mar 2, 1998• 53 citations

arXiv HTML PDF

Abstract

\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

\mathrm{XY}

universality,

{\ensuremath{\nu}}_{\mathrm{XY}}\ensuremath{\approx}2/3

. Our results confirm the anomalous scaling dimension of magnetic field correlations at

{T}_{c}

DOI: 10.1103/physrevlett.80.1964

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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 $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.51$ for the isotropic London lattice model.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.

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\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

\mathrm{XY}

universality,

{\ensuremath{\nu}}_{\mathrm{XY}}\ensuremath{\approx}2/3

. Our results confirm the anomalous scaling dimension of magnetic field correlations at

{T}_{c}

z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.51

for the isotropic London lattice model.

We present a Monte Carlo study of the Bose glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical

(3+1)

dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as $16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}16\ifmmode\times\else\texttimes\fi{}512$ sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent

z=3

, in agreement with existing scaling and renormalization group arguments that

z=d

. We find also a value of $\ensuremath{\nu}=0.70(12)$ for the correlation length exponent, satisfying the relation $\ensuremath{\nu}\ensuremath{\ge}2∕d$. However, a detailed study of the correlation functions, $C(r,\ensuremath{\tau})$, at the quantum critical point are not consistent with this value of

z

. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.

We have used Monte Carlo simulations, combined with finite-size scaling and two different real-space renormalization group approaches, to study a fully frustrated three-dimensional

XY

model on a simple cubic lattice. This model corresponds to a lattice of Josephson-coupled superconducting grains in an applied magnetic field $\mathbf{H}=({\ensuremath{\Phi}}_{0}∕{a}^{2})(1∕2,1∕2,1∕2)$. We find that the model has a continuous phase transition with critical temperature

{T}_{c}=0.681\phantom{\rule{0.3em}{0ex}}J∕{k}_{B}

, where

J

is the

XY

coupling constant, and critical exponents $\ensuremath{\alpha}∕\ensuremath{\nu}=0.87\ifmmode\pm\else\textpm\fi{}0.01$, $v∕\ensuremath{\nu}=0.82\ifmmode\pm\else\textpm\fi{}0.01$, and $\ensuremath{\nu}=0.72\ifmmode\pm\else\textpm\fi{}0.07$, where $\ensuremath{\alpha}$,

v

, and $\ensuremath{\nu}$ describe the critical behavior of the specific heat, helicity modulus, and correlation length. We briefly compare our results with other studies of this model, and with a mean-field approximation.