Anomalous dimensions and phase transitions in superconductors

Abstract

The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $\eta$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $\eta$ comes from the divergence of the critical correlation function at finite distances. This behavior implies the existence of a Lifshitz point in the phase diagram. The anomalous scaling of the vector potential is also discussed. It is shown that the anomalous dimension of the vector potential ${\eta }_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $\sigma (\omega )\sim {\xi }^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.

RevTex, 20 pages, no figures; small changes; version accepted in PRB

References in corpus (5)

• Anomalous scaling dimensions and stable charged fixed-point of type-II superconductors
• Hausdorff dimension of critical fluctuations in abelian gauge theories
• Scaling critical behavior of superconductors at zero magnetic field
• Critical scaling of the a.c. conductivity for a superconductor above Tc
• Anomalous scaling dimensions and critical points in type-II superconductors

Cited by in corpus (11)

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• Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter $\kappa$
• Critical behavior of Ginzburg-Landau model coupled to massless Dirac fermions
• Methods to determine the Hausdorff dimension of vortex loops in the three-dimensional XY model
• Gauge-invariant critical exponents for the Ginzburg-Landau model
• Bulk and Boundary Critical Behavior at Lifshitz Points
• Hamiltonian Study of Improved $U(1$ Lattice Gauge Theory in Three Dimensions
• Critical dynamics, duality, and the exact dynamic exponent in extreme type II superconductors
• Three-Loop Ground-State Energy of O(N)-Symmetric Ginzburg-Landau Theory Above T_c in 4-epsilon Dimensions with Minimal Subtraction
• Fermion zero mode and superfluid weight