Large-Order Behavior of the Perturbation Series for Superconductors near<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mn>2</mml:mn><mml:mn /></mml:mrow></mml:msub></mml:mrow></mml:math>

Brézin, E.; Fujita, Atsuko; Hikami, Shinobu

doi:10.1103/physrevlett.65.1949

Cited by 95 publications

(31 citation statements)

References 15 publications

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“…One can compare the results with existing (not very extensive) Monte Carlo simulation and agreement is well within the MC precision. Moreover similar method was applied to the 2D GL model which was simulated extensively (Hu and MacDonald, 1993;Hu et al, 1994;Kato and Nagaosa, 1993;O'Neill and Moore, 1993;Tešanović and Xing, 1991) and for which longer series are available (Brézin et al, 1990;Hikami et al, 1991) and agreement is still perfect. We conclude that the method is precise enough to study the melting problem.…”

Section: Comparison With Other Resultsmentioning

confidence: 99%

“…Attempts to use BP for calculation of melting also ran into problems. Hikami, Fujita and Larkin (Brézin et al, 1990;Hikami et al, 1991) tried to find the melting point by comparing the BP energy with the one loop solid energy and obtained a T = −7. However their one loop solid energy was incorrect (by factor √ 2) and in any case it was not precise enough, since the two loop contribution is essential.…”

Section: Comparison With Other Resultsmentioning

confidence: 99%

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Ginzburg-Landau theory of type II superconductors in magnetic field

2010

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Thermodynamics of type II superconductors in electromagnetic field based on the GinzburgLandau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor -normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high Tc materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg -Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose -Einstein condensate.

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Section: Comparison With Other Resultsmentioning

confidence: 99%

Section: Comparison With Other Resultsmentioning

confidence: 99%

Ginzburg-Landau theory of type II superconductors in magnetic field

2010

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“…Since fluctuations become more important with reduced dimensionality and there is the limiting magnetic length scale L H it becomes clear that the upper critical field H c2 is an artefact of the approximations. Indeed, calculations of the specific heat in a magnetic field which treat the interaction terms in the Hartree approximation and extensions thereof, find that the specific heat is smooth through the mean-field transition temperature T c2 (H) [7,8,9]. In the context of finite size scaling this is simply due to the fact that the correlation length of fluctuations which are transverse to the applied magnetic field are bounded by the magnetic length L H ∝ H −1/2 .…”

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confidence: 99%

Magnetic field induced 3D–1D crossover in type-II superconductors

Schneider

2008

J. Phys.: Condens. Matter

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Abstract. We review and analyze magnetization and specific heat investigations on type-II superconductors which uncover remarkable evidence for the magnetic field induced finite size effect and the associated 3D to 1D crossover which enhances thermal fluctuations. Indeed, the correlation length transverse to the magnetic field H i , applied along the i-axis, cannot grow beyond the limiting magnetic length1/2 , related to the average distance between vortex lines. Noting that 1D is incompatible with the occurrence of a continuous phase transition at finite temperatures, the mean-field transition line H C2 (T ) is replaced by the 3D to 1D crossover line Hp (T ). Since the magnetic field induced finite size effect relies on thermal fluctuations and there enhancement originating from the 3D to 1D crossover, its observability is not be restricted to type-II superconductors with small correlation volume only, including YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ , where 3D-xy critical behavior was already observed in zero field. Indeed, our analysis of the reversible magnetization of RbOs 2 O 6 and the specific heat of Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 reveals that even in these low Tc superconductors with comparatively large correlation volume the 3D to 1D crossover is observable in sufficiently high magnetic fields. Consequently, below Tc and above H pi (T ) superconductivity is confined to cylinders with diameter L H i (1D) and there is no continuous phase transition in the (H, T ) -plane along the H c2 (T ) -line as predicted by the mean-field treatment. Moreover we observe that the thermodynamic vortex melting transition occurs in the 3D regime. While in YBa 2 Cu 4 O 8 , NdBa 2 Cu 3 O 7−δ , YBa 2 Cu 3 O 7−δ , and DyBa 2 Cu 3 O 7−δ it turns out to be driven by 3D-xy thermal fluctuations, the specific heat data of the conventional type-II superconductors Nb 77 Zr 23 , Nb 3 Sn and NbSe 2 point to Gaussian fluctuations. Because the vortex melting and the 3D-1D crossover line occur at universal values of the scaling variable their relationship is universal.

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“…The coefficients can be found in ref. [24,25]. We will denote g k (x) by the [k, k − 1] BP transform of g(x) (other BP approximants clearly violate the correct low temperature asymptotics).…”

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confidence: 99%

Melting of the vortex lattice in high−Tcsuperconductors

Rosenstein

2002

Phys. Rev. B

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Large-Order Behavior of the Perturbation Series for Superconductors nearHc2

Cited by 95 publications

References 15 publications

Ginzburg-Landau theory of type II superconductors in magnetic field

Ginzburg-Landau theory of type II superconductors in magnetic field

Magnetic field induced 3D–1D crossover in type-II superconductors

Melting of the vortex lattice in high−Tcsuperconductors

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