April 5, 1995
An effective field theory is derived for the ferromagnetic transition of diffusive electrons at T=0. The static disorder which leads to diffusive electron dynamics induces an effective long-range interaction between the spins of the form 1/r^(2d-2). This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. The crossover from this quantum fixed point to the classical Heisenberg fixed point should be observable in ferromagnetic materials with low Curie temperatures.
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January 3, 1996
The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the spin or order parameter fluctuations of the form r^{2-2d}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. In three-dimensional systems the quantum critical e...
October 24, 2000
The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition sho...
December 24, 1996
We consider the quantum ferromagnetic transition at zero temperature in clean itinerant electron systems. We find that the Landau-Ginzburg-Wilson order parameter field theory breaks down since the electron-electron interaction leads to singular coupling constants in the Landau-Ginzburg-Wilson functional. These couplings generate an effective long-range interaction between the spin or order parameter fluctuations of the form 1/r^{2d-1}, with d the spatial dimension. This leads...
December 30, 2002
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets as the transition is approached from the ferromagnetic phase. This complements a recent study of the critical behavior on the paramagnetic side of the phase transition, and investigates the role of the ferromagnetic Goldstone modes near criticality. We find that the Goldstone modes have no direct impact on the critical behavior, and that the critical exponents are the s...
September 6, 1996
The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard Landau-Ginzburg-Wilson description of this transition. If these modes are taken into account, then the resulting order parameter field theory is nonlocal in space and time. Nevertheless, for both disordered and clean systems the critical behavior has been exact...
August 3, 2000
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets in the presence of quenched disorder. In contrast to previous approaches, all soft modes are kept explicitly. The resulting effective theory is local and allows for an explicit perturbative treatment. It is shown that previous suggestions for the critical fixed point and the critical behavior are recovered under certain assumptions. The validity of these assumptions is ...
December 29, 1999
The theory for disordered itinerant ferromagnets developed in a previous paper is used to construct a simple effective field theory that is capable of describing the quantum phase transition from a ferromagnetic metal to a ferromagnetic insulator. It is shown that this transition is in the same universality class as the one from a paramagnetic metal to a paramagnetic insulator in the presence of an external magnetic field, and that strong corrections to scaling exist in this ...
July 26, 1999
We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective long-range interaction between the spin fluctuations. This interaction turns out to be generically {\em antiferromagnetic} for clean systems. In disordered systems analogous correlation effects lead to even stronger singularities. The resulti...
November 1, 1999
Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quan...
October 25, 1995
The quantum ferromagnetic transition of itinerant electrons is considered. It is shown that the Landau-Ginzburg-Wilson theory described by Hertz and others breaks down due to a singular coupling between fluctuations of the conserved order parameter. This coupling induces an effective long-range interaction between the spins of the form 1/r^{2d-1}. It leads to unusual scaling behavior at the quantum critical point in $1<d\leq 3$ dimensions, which is determined exactly.