arXiv subjects
Publications and source records attributed to Flavio S. Nogueira.
We point out interesting effects of additional massless Dirac fermions with N_F colors upon the critical behavior of the Ginzburg-Landau model. For increasing N_F, the model is driven into the type II regime of superconductivity. The critical exponents are given as a function of N_F.
The large N analysis of an extreme type II superconductor is revisited. It is found that the phase transition is of second-order in dimensions 4 < d < 6. For the physical dimension d=3 no sign of phase transition is found, contrary to early claims.
The Ginzburg-Landau model with a Chern-Simons term is shown to possess two different scaling regimes depending on whether the mass of the scalar field is zero or not. In contrast to pure $ϕ^4$ theories, the Ginzburg-Landau model with a topologically generated mass exhibits quite different properties in perturbation theory. Our analysis suggests that the two scalings could coincide at a non-perturbative level. This view is supported by a 1/N-expansion in the massive scalar field regime.
We derive the exact dual theory of a lattice Ginzburg-Landau theory with an additional topological Chern-Simons (CS) term. It is shown that in the zero-temperature limit, the statistical parameter $θ=1/2π$ corresponds to a fixed point of the duality transformation. Thus we have found a nontrivial example of self-duality in three dimensions. In this scenario, the specialization of anyonic to fermionic statistics my be viewed as a phase transition.
The anomalous scaling in the Ginzburg-Landau model for the superconducting phase transition is studied. It is argued that the negative sign of the $η$ exponent is a consequence of a special singular behavior in momentum space. The negative sign of $η$ 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 $η_A=4-d$ has important consequences for the critical dynamics in superconductors. The frequency-dependent conductivity is shown to obey the scaling $σ(ω)\simξ^{z-2}$. The prediction $z\approx 3.7$ is obtained from existing Monte Carlo data.
An unifying scenario for the critical behavior of YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (BSCCO) is proposed. It is shown that both critical crossovers observed in these materials follow by considering two different scalings in the dual Ginzburg-Landau model. The first scaling leads to the critical exponents $ν\approx 2/3$, $ν'\approx 1/3$ and $α\approx 0$, with $ν$ and $α$ being respectively the correlation lenght and specific heat exponents while $ν'$ is the magnetic field penetration depth exponent. These values for the critical exponents agree with the ones obtained experimentally for YBCO single crystals. For the second scaling we obtain $ν=1$ and $α=-1$ which must be compared with the measured values $ν\approx 1$ and $α\approx-0.7$ for BSCCO. For the penetration depth exponent it is predicted the value $ν'=1$.
The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the local superconducting order parameter, it is shown that its exponent $β$ is in fact gauge independent. This happens because in $d=3$ the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gauge choice is possible. The analysis is done in both the context of the $ε$-expansion and in the fixed dimension approach. It is pointed out the differences that arise in both of these approaches concerning the gauge dependence.
The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the superconducting order parameter, it is shown that its exponent $β$ is in fact gauge independent. This happens because in d=3 the Landau gauge is the only gauge having a physical meaning, a property not shared by the four-dimensional model where any gauge choice is possible. The analysis is done in both the context of the $ε$-expansion and in the fixed dimension approach. It is pointed out the differences that arise in both of these approaches concerning the gauge dependence.
The N component scalar tricritical theory is considered in a non-perturbative setting. We derive non-perturbative beta functions for the relevant couplings in $d\leq 3$. The beta functions are obtained through the use of an exact evolution equation for the so called effective average action. In d=3 it is established the existence of an ultraviolet stable fixed point for N>4. This confirms earlier results obtained using the 1/N expansion where such a fixed point is believed to exist at least for $N\gtrsim 1000$.
A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping is established the equivalence of the model with the Hubbard model with infinite range hopping. The generalization to the case with $N$ components is made.