D. Belitz

How generic scale invariance influences quantum and classical phase transitions

This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions; namely, the coupling of the order-parameter fluctuations to other soft modes, and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance, and its influence on critical behavior, is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include: the quantum ferromagnetic transition in metals, with or without quenched disorder; the metalsuperconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.

First Order Transitions and Multicritical Points in Weak Itinerant Ferromagnets

It is shown that the phase transition in low-T_c clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical endpoint. A semi-quantitative discussion is given in terms of recent experiments on MnSi, and predictions for other experiments are made.

Tricritical Behavior in Itinerant Quantum Ferromagnets

It is shown that the peculiar features observed in the low-temperature phase diagrams of ZrZn_2, UGe_2, and MnSi can be understood in terms of a simple mean-field theory. The nature of the ferromagnetic transition changes from second order to first order at a tricritical point, and in a small external magnetic field surfaces of first-order transitions emerge which terminate in quantum critical points. This field dependence of the phase diagram follows directly from the existence of the tricritical point. The quantum critical behavior in a nonzero field is calculated exactly.

Strong Enhancement of SuperconductingTcin Ferromagnetic Phases

It is shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of the magnons to the longitudinal magnetic susceptibility. Together with the tendency of the low-temperature ferromagnetic transition in very clean Heisenberg magnets to be of first order, this qualitatively explains the phase diagram recently observed in UGe(2).

Metallic quantum ferromagnets

This work has been supported by the National Science Foundation under grant numbers NSF DMR-09-29966, DMR-09-01907, DMR-1401410, and DMR-1401449, and by the Deutsche Forschungsgemeinschaft under grant number FOR-960. Part of this work has been supported by the National Science Foundation under Grant. No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.

Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wave vector and temperature-dependent static spin susceptibility,

Self-consistent current relaxation theory for the electron localization problem

{\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}

Theory of phonon-controlled conductivity in high-resistivity conductors

(Q,T), of clean interacting Fermi systems is considered in dimensions 1\ensuremath{\leqslant}d\ensuremath{\leqslant}3. We show that at zero temperature

Quantum critical behavior of disordered itinerant ferromagnets

{\mathrm{\ensuremath{\chi}}}_{\mathrm{s}}

Theory of helimagnons in itinerant quantum systems

is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q