Physical Review B

Nonequilibrium phase transition in fully frustrated Josephson junction arrays: A short-time dynamic approach

Qingmiao Nie, Meng‐Bo Luo, Qing‐Hu Chen

Published Jul 27, 2006• 11 citations

Abstract

The nonequilibrium phase transition of two-dimensional fully frustrated Josephson junction arrays driven by external currents is studied in the framework of the short-time dynamic scaling approach. Within the resistively shunted junction dynamics, besides the critical temperature ${T}_{c}$, the static and dynamic critical exponents $2\ensuremath{\beta}∕\ensuremath{\nu}$, $\ensuremath{\nu}$, and $z$ are obtained. The resulting values of ${T}_{c}$ are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent $\ensuremath{\nu}$ are not sensitive to external currents, while the values of $2\ensuremath{\beta}∕\ensuremath{\nu}$ and $z$ are strongly current dependent.

DOI: 10.1103/physrevb.74.024523

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Physical Review B

Nonequilibrium phase transition in fully frustrated Josephson junction arrays: A short-time dynamic approach

Qingmiao Nie, Meng‐Bo Luo, Qing‐Hu Chen

Published Jul 27, 2006• 11 citations

Publisher

Abstract

{T}_{c}

, the static and dynamic critical exponents

2\ensuremath{\beta}∕\ensuremath{\nu}

\ensuremath{\nu}

, and

z

are obtained. The resulting values of

{T}_{c}

are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent

\ensuremath{\nu}

are not sensitive to external currents, while the values of

2\ensuremath{\beta}∕\ensuremath{\nu}

and

z

are strongly current dependent.

DOI: 10.1103/physrevb.74.024523

Related papers

Non-equilibrium Phase Transition of Two-dimensional Fully-frustrated Josephson Junction Arrays

Ying Guo

Acta Physico-Chimica SinicaJan 1, 20070 citations

Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder

Jaegon Um, Beom Jun Kim, Petter Minnhagen +2 more

We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of ${E}_{J}∕{k}_{B}$ with the Josephson coupling strength ${E}_{J}$ ), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current-voltage characteristics reveals evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of ${E}_{J}∕{k}_{B}$ with the Josephson coupling strength ${E}_{J}$), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.

arXiv:cond-mat/0608390Physical Review BSep 28, 200610 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.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 LettersDec 1, 20032 citations

Current-voltage characteristics of diluted Josephson-junction arrays: Scaling behavior at current and percolation threshold

Enzo Granato, Daniel Domı́nguez

Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where ${p}_{c}$ is the percolation threshold. For $p>{p}_{c}$ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At ${p}_{c}$ and finite temperature $T,$ the results show the scaling behavior of a $T=0$ superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted $\mathrm{XY}$ model at ${p}_{c}.$ Dynamical simulations and scaling arguments are used to study the current-voltage $(I\ensuremath{-}V)$ characteristics of a two-dimensional model of resistively shunted Josephson-junction arrays in presence of percolative disorder, at zero external field. Two different limits of the Josephson-coupling concentration $p$ are considered, where ${p}_{c}$ is the percolation threshold. For $p>{p}_{c}$ and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At ${p}_{c}$ and finite temperature $T,$ the results show the scaling behavior of a $T=0$ superconducting transition. The resistance is linear but vanishes for decreasing $T$ with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted $\mathrm{XY}$ model at ${p}_{c}.$

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Qing‐Hu Chen, Meng-Bo Luo, Zhengkuan Jiao

The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated $\mathrm{XY}$ model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings is investigated using Monte Carlo simulations. When $x<1/\sqrt{2}$ $(x$ is the ratio between NNN and NN couplings), the transition temperature ${T}_{c}$ and the dynamic and static critical exponents z, $2\ensuremath{\beta}/\ensuremath{\nu},$ and $\ensuremath{\nu}$ are estimated using the short-time dynamic scaling analysis. Except x close to the critical value $1/\sqrt{2},$ the critical exponents $2\ensuremath{\beta}/\ensuremath{\nu}$ and $\ensuremath{\nu}$ are found to be almost independent of the NNN coupling, indicating that the second-order phase transitions in the $\mathrm{FF}\mathrm{XY}$ model, with or without NNN coupling, are in the same universality class. When $x>1/\sqrt{2},$ the short-time dynamic study suggests that there is no second-order phase transition, in agreement with the previous result [Phys. Rev. B 62, R9287 (2000)].The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated $\mathrm{XY}$ model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings is investigated using Monte Carlo simulations. When $x<1/\sqrt{2}$ $(x$ is the ratio between NNN and NN couplings), the transition temperature ${T}_{c}$ and the dynamic and static critical exponents z, $2\ensuremath{\beta}/\ensuremath{\nu},$ and $\ensuremath{\nu}$ are estimated using the short-time dynamic scaling analysis. Except x close to the critical value $1/\sqrt{2},$ the critical exponents $2\ensuremath{\beta}/\ensuremath{\nu}$ and $\ensuremath{\nu}$ are found to be almost independent of the NNN coupling, indicating that the second-order phase transitions in the $\mathrm{FF}\mathrm{XY}$ model, with or without NNN coupling, are in the same universality class. When $x>1/\sqrt{2},$ the short-time dynamic study suggests that there is no second-order phase transition, in agreement with the previous result [Phys. Rev. B 62, R9287 (2000)].

Physical review. B, Condensed matterNov 8, 200115 citations

Modeling bond dilutions in Josephson junction arrays

Jian-Ping Lv, Qing-Hu Chen

Using resistivity-shunted-junction dynamics, we model bond dilutions in Josephson junction arrays. The current-voltage characteristics are obtained by large-scale numerical simulations. By dynamic scaling analysis to the finite-temperature phase transition, we provide clear evidence for the existence of non-Kosterlitz–Thouless-type phase transition, as described by Kosterlitz et al. [J. Phys. C 6, 1181 (1973); J. Phys. C 7, 1046 (1974)] in a wide range of disorder strengths. Critical temperature and exponents of the phase transitions are estimated, which are further confirmed by the finite-size scaling analysis at the transition temperature.Using resistivity-shunted-junction dynamics, we model bond dilutions in Josephson junction arrays. The current-voltage characteristics are obtained by large-scale numerical simulations. By dynamic scaling analysis to the finite-temperature phase transition, we provide clear evidence for the existence of non-Kosterlitz–Thouless-type phase transition, as described by Kosterlitz et al. [J. Phys. C 6, 1181 (1973); J. Phys. C 7, 1046 (1974)] in a wide range of disorder strengths. Critical temperature and exponents of the phase transitions are estimated, which are further confirmed by the finite-size scaling analysis at the transition temperature.

Applied Physics LettersMar 7, 20111 citation

{T}_{c}

, the static and dynamic critical exponents

2\ensuremath{\beta}∕\ensuremath{\nu}

\ensuremath{\nu}

, and

z

are obtained. The resulting values of

{T}_{c}

are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent

\ensuremath{\nu}

are not sensitive to external currents, while the values of

2\ensuremath{\beta}∕\ensuremath{\nu}

and

z

are strongly current dependent.

{E}_{J}∕{k}_{B}

with the Josephson coupling strength

{E}_{J}

), the correlation length critical exponent $\ensuremath{\nu}=1.2$, and the dynamic critical exponent

z=2.0

in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.

p

are considered, where

{p}_{c}

is the percolation threshold. For

p>{p}_{c}

and zero temperature, the $I\ensuremath{-}V$ curves show power-law behavior above a disorder-dependent critical current. The power-law behavior and critical exponents are consistent with a simple scaling analysis. At

{p}_{c}

and finite temperature

T,

the results show the scaling behavior of a

T=0

superconducting transition. The resistance is linear but vanishes for decreasing

T

with an apparent exponential behavior. Crossover to nonlinearity appears at currents proportional to ${T}^{1+{\ensuremath{\nu}}_{T}},$ with a thermal-correlation length exponent ${\ensuremath{\nu}}_{T}$ consistent with the corresponding value for the diluted

\mathrm{XY}

model at

{p}_{c}.

The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated

\mathrm{XY}

model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings is investigated using Monte Carlo simulations. When

x<1/\sqrt{2}

(x

is the ratio between NNN and NN couplings), the transition temperature

{T}_{c}

and the dynamic and static critical exponents z, $2\ensuremath{\beta}/\ensuremath{\nu},$ and $\ensuremath{\nu}$ are estimated using the short-time dynamic scaling analysis. Except x close to the critical value

1/\sqrt{2},

the critical exponents $2\ensuremath{\beta}/\ensuremath{\nu}$ and $\ensuremath{\nu}$ are found to be almost independent of the NNN coupling, indicating that the second-order phase transitions in the

\mathrm{FF}\mathrm{XY}

model, with or without NNN coupling, are in the same universality class. When

x>1/\sqrt{2},

the short-time dynamic study suggests that there is no second-order phase transition, in agreement with the previous result [Phys. Rev. B 62, R9287 (2000)].