Scaling critical behavior of superconductors at zero magnetic field

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The first part of the paper is concerned with the Ginzburg-Landau model in the zero magnetic field Meissner phase. We discuss the scaling behavior of the superfluid density and we give an alternative proof of Josephson's relation for a charged superfluid. This proof is obtained as a consequence of an exact renormalization group equation for the photon mass. We obtain Josephson's relation directly in the form $\rho_{s}\sim t^{\nu}$, that is, we do not need to assume that the hyperscaling relation holds. Next, we give an interpretation of a recent experiment performed in thin films of $YBa_{2}Cu_{3}O_{7-\delta}$. We argue that the measured mean field like behavior of the penetration depth exponent $\nu'$ is possibly associated with a non-trivial critical behavior and we predict the exponents $\nu=1$ and $\alpha=-1$ for the correlation lenght and specific heat, respectively. In the second part of the paper we discuss the scaling behavior in the continuum dual Ginzburg-Landau model. After reviewing lattice duality in the Ginzburg-Landau model, we discuss the continuum dual version by considering a family of scalings characterized by a parameter $\zeta$ introduced such that $m_{h,0}^2\sim t^{\zeta}$, where $m_{h,0}$ is the bare mass of the magnetic induction field. We discuss the difficulties in identifying the renormalized magnetic induction mass with the photon mass. We show that the only way to have a critical regime with $\nu'=\nu\approx 2/3$ is having $\zeta\approx 4/3$, that is, with $m_{h,0}$ having the scaling behavior of the renormalized photon mass.Comment: RevTex, 15 pages, no figures; the subsection III-C has been removed due to a mistak

Anomalous dimensions and phase transitions in superconductors

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.Comment: RevTex, 20 pages, no figures; small changes; version accepted in PR

RI'/SMOM scheme amplitudes for quark currents at two loops

We determine the two loop corrections to the Green's function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the MSbar and RI'/SMOM renormalization schemes. The RI'/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov-Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI'/SMOM scheme in the case of the tensor current.Comment: 36 latex pages, 1 figure, 21 tables, anc directory contains txt file with data in table

Diet of two syntopic species of Crenuchidae (Ostariophysi: Characiformes) in an Amazonian rocky stream

Abstract This study assessed the diet of two poorly known syntopic fish species of the family Crenuchidae, Characidium aff. declivirostre and Leptocharacidium omospilus, in a Presidente Figueiredo´ rocky stream, Amazonas, Brazil. The stomach contents were analyzed and their Frequency of Occurrence (FO %) and Relative Volume (Vol %) were combined in a Feeding Index (IAi). We examined 20 individuals of C. aff. declivirostre and 23 of L. omospilus. The Morisita-Horn Index was used to estimate the overlap between the diets of these species. Immature insects were the most valuable items consumed by both fish species. The diet of C. aff. declivirostre was mainly composed of larvae and pupae of Chironomidae, while L. omospilus predominantly consumed larvae of Hydroptilidae, Hydropyschidae and Pyralidae. Thus, both species were classified as autochthonous insectivorous. Characidium aff. declivirostre was considered a more specialized species, probably reflecting lower feeding plasticity or the use of more restricted microhabitats compared to L. omospilus. When the food items were analyzed at the family taxonomic level, the diet overlap between these species was considered moderate (Morisita-Horn Index = 0.4). However, a more thorough analysis, at the genus level, indicates a very low diet overlap. Therefore, we conclude that the feeding segregation between C. aff. declivirostre and L. omospilus may favor their co-existence, despite their high phylogenetic closeness