Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets

A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-\epsilon$ expansion.Comment: 15 pp., revtex4, 6 eps figs; final version as publishe

Transport properties of clean and disordered superconductors in matrix field theory

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin density susceptibility and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal metal state and the superconductor state.Comment: 9 page

Fluctuation-Driven Quantum Phase Transitions in Clean Itinerant Ferromagnets

The quantum phase transition in clean itinerant ferromagnets is analyzed. It is shown that soft particle-hole modes invalidate Hertz's mean-field theory for $d \leq 3$. A renormalized mean-field theory predicts a fluctuation-induced first order transition for $1 < d \leq 3$, whose stability is analyzed by renormalization group techniques. Depending on microscopic parameter values, the first order transition can be stable, or be pre-empted by a fluctuation-induced second order transition. The critical behavior at the latter is determined. The results are in agreement with recent experiments.Comment: 4 pp., REVTeX, no figs; final version as publishe

Electrons in an annealed environment: A special case of the interacting electron problem

The problem of noninteracting electrons in the presence of annealed magnetic disorder, in addition to nonmagnetic quenched disorder, is considered. It is shown that the proper physical interpretation of this model is one of electrons interacting via a potential that is long-ranged in time, and that its technical analysis by means of renormalization group techniques must also be done in analogy to the interacting problem. As a result, and contrary to previous claims, the model does not simply describe a metal-insulator transition in $d=2+\epsilon$ ($\epsilon\ll 1$) dimensions. Rather, it describes a transition to a ferromagnetic state that, as a function of the disorder, precedes the metal-insulator transition close to $d=2$. In $d=3$, a transition from a paramagnetic metal to a paramagnetic insulator is possible.Comment: 13 pp., LaTeX, 2 eps figs; final version as publishe

Electronic Transport at Low Temperatures: Diagrammatic Approach

We prove that a diagrammatic evaluation of the Kubo formula for the electronic transport conductivity due the exchange of bosonic excitations, in the usual conserving ladder approximation, yields a result consistent with the Boltzmann equation. In particular, we show that an uncontrolled approximation that has been used to solve the integral equation for the vertex function is unnecessary. An exact solution of the integral equation yields the same asymptotic low-temperature behavior as the approximate one, albeit with a different prefactor, and agrees with the temperature dependence of the Boltzmann solution. Examples considered are electron scattering from acoustic phonons, and from helimagnons in helimagnets.Comment: Submitted to Physics E (FMQT08 Proceedings). Requires Elsevier style file (included

Local versus Nonlocal Order Parameter Field Theories for Quantum Phase Transitions

General conditions are formulated that allow to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson or LGW theory solely in terms of the order parameter. A crucial question is the degree to which the order parameter fluctuations couple to other soft modes. Three general classes of zero-wavenumber order parameters, in the particle-hole spin-singlet and spin-triplet channels, and in the particle-particle channel, respectively, are considered. It is shown that the particle-hole spin-singlet class does allow for a local LGW theory, while the other two classes do not. The implications of this result for the critical behavior at various quantum phase transitions are discussed, as is the connection with nonanalyticities in the wavenumber dependence of order parameter susceptibilities in the disordered phase.Comment: 9 pp., LaTeX, no figs, final version as publishe

Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies \Omega, small wavevectors k, and small m, the dispersion relation is found to be of the form \Omega ~ m^{1-\alpha} k^2, with \alpha = (4-d)/2 (2<d<4) for disordered systems, and \alpha = (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), \Omega ~ m ln(1/m) k^2. Experiments to test these predictions are proposed.Comment: 4 pp., REVTeX, no fig

Properties of spin-triplet, even-parity superconductors

The physical consequences of the spin-triplet, even-parity pairing that has been predicted to exist in disordered two-dimensional electron systems are considered in detail. We show that the presence of an attractive interaction in the particle-particle spin-triplet channel leads to an instability of the normal metal that competes with the localizing effects of the disorder. The instability is characterized by a diverging length scale, and has all of the characteristics of a continuous phase transition. The transition and the properties of the ordered phase are studied in mean-field theory, and by taking into account Gaussian fluctuations. We find that the ordered phase is indeed a superconductor with an ordinary Meissner effect and a free energy that is lower than that of the normal metal. Various technical points that have given rise to confusion in connection with this and other manifestations of odd-gap superconductivity are also discussed.Comment: 15 pp., REVTeX, psfig, 2 ps figs, final version as publishe