Common universality class for the three-dimensional vortex glass and chiral glass

Wengel, Carsten; Young, A. P.

doi:10.1103/physrevb.56.5918

Cited by 60 publications

(73 citation statements)

References 22 publications

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“…However the situation is less conclusive, since the simulations are limited to small system sizes. Finite temperature Monte Carlo studies yield a transition temperature T c /J ∼ O(1) 4,5,13 which is difficult to reconcile with DWRG studies 5,6,8,9 as these studies imply that the lower critical dimension for superconducting glass order is close to three. Experimentally there is also some evidence for a finite temperature phase transition to a superconducting glass phase 14,15 .…”

Section: Introductionmentioning

confidence: 96%

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Akino

Kosterlitz

2002

Phys. Rev. B

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The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents θs ≈ −0.36 in 2D and θs ≈ +0.31 in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the ±J XY spin glass in 3D, we obtain a spin stiffness exponent θs ≈ +0.10 which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain θs < 0. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

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Section: Introductionmentioning

confidence: 96%

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Akino

Kosterlitz

2002

Phys. Rev. B

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“…These simulations were based on different dynamics and different representations of the same XY-spin glass model. While the static exponents agree, as expected from the universality of critical behavior, the dynamic exponent z ∼ 4.6 obtained from the resistivelyshunted-junction (RSJ) model of the dynamics in the phase representation [12] is significantly different from that obtained from MC dynamics, z ∼ 3.1, in the vortex representation [11], suggesting a strong dependence of z on the details of the dynamics. In view of the absence of precise agreement among these studies, additional numerical results using different dynamics are required to confirm the resistive behavior and determine the critical properties satisfactorily.…”

mentioning

confidence: 86%

“…More recent, improved calculations in the vortex representation, also clearly shows a large and positive stiffness exponent [16]. In addition, calculations of the linear resistivity ρ L (zero current bias) from MC dynamics simulations in the vortex representation [11], shows an equilibrium resistive transition. The estimate of the static exponent ν agrees with the present estimate from the nonlinear resistivity but the dynamic exponent [11] z = 3.1 is significantly lower.…”

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confidence: 99%

“…The first term gives the nearest-neighbor Josephson coupling energy, where the quenched phase shift t ij is equal to π or 0 with equal probabilities, corresponding to the standard ±J o XY spin glass model [6,7,9,10,12,11]. The second term in Eq.…”

mentioning

confidence: 99%

“…In fact, numerical simulations of the resistive behavior in two dimensions shows that the transition occurs at zero temperature [10]. In three dimensions, dynamical simulations suggest a resistive transition at finite temperatures [11,12]. These simulations were based on different dynamics and different representations of…”

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confidence: 99%

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Numerical study of resistivity scaling in pi junction granular superconductors

Granato¹

2003

Braz. J. Phys.

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Numerical simulations based on Monte Carlo dynamics are used to investigate the resistivity behavior of granular superconductors containing a random distribution of π junctions, as in superconducting materials with d-wave symmetry. The presence of π junctions leads to quenched in circulating currents (chiralities) and to chiral glass behavior at low temperatures, even without an external magnetic field. An XY spin glass model in the phase representation is used to determine the current-voltage characteristics and critical exponents of the resistivity transition. In two dimensions, the linear resistivity is nonzero at finite temperatures and the dynamic scaling analysis of the nonlinear resistivity is consistent with a phase transition at zero temperature. In three dimensions, we find a transition at finite temperatures below which the linear resistivity vanishes and the corresponding critical exponents are determined from the scaling analysis. The results are in good agreement with Langevin simulations in the phase representation. The dynamic exponent z is significantly different from previous results obtained in the vortex representation.Granular superconductors with d-wave symmetry, as some of the unconventional high-T c superconducting materials, can be viewed as a network of Josephson junctions with frustration effects even in zero external magnetic field [1]. Frustration arises from the presence of π junctions which introduce a phase shift of π between superconducting regions, and to half-flux quantum vortices on closed loops with an odd number of these junctions [2,3]. The magnetic properties of granular samples, arising from the orbital currents of theses vortices , have been extensively studied [1,4,5,6,7] and provide an explanation of the paramagnetic Meissner effect [8]. Nevertheless, there are also important consequences for the resistivity behavior of theses systems which also deserve detailed investigations.In a conventional granular superconductor, the phases of neighboring superconducting regions tend to be locked with zero phase shift, and a phase-coherence transition is expected for decreasing temperature into a superconducting state with vanishing linear resistivity. The critical behavior of this resistive transition is reasonable well understood both in the two dimensional limit and in three dimensions. On the other hand, for granular superconductors with a large concentration of π junctions, frustration and disorder effects leads to a vortex glassy phase and the resistive behavior is much less understood. The simplest model of the system is to consider only contributions from the Josephson coupling energy of nearest-neighbor grains,, where θ i is the phase of the local superconducting order parameter, J o > 0 and t ij = 0 or π correspond to the phase shifts of 0 and π junctions. This is equivalent to the interaction of two-component pseudo-spins S = (cos(θ), sin(θ)), coupled by ferro or antiferromagnetic interactions, respectively, which leads to an XY-spin (chiral) glass model for the granul...

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Spin Glasses

Kawamura

Taniguchi

2015

Handbook of Magnetic Materials

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Common universality class for the three-dimensional vortex glass and chiral glass

Cited by 60 publications

References 22 publications

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Numerical study of resistivity scaling in pi junction granular superconductors

Spin Glasses

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