Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.Comment: 9 pages, 2 figure

Transport properties in antiferromagnetic quantum Griffiths phases

We study the electrical resistivity in the quantum Griffiths phase associated with the antiferromagnetic quantum phase transition in a metal. The resistivity is calculated by means of the semi-classical Boltzmann equation. We show that the scattering of electrons by locally ordered rare regions leads to a singular temperature dependence. The rare-region contribution to the resistivity varies as $T^\lambda$ with temperature $T,$ where the $\lambda$ is the usual Griffiths exponent which takes the value zero at the critical point and increases with distance from criticality. We find similar singular contributions to other transport properties such as thermal resistivity, thermopower and the Peltier coefficient. We also compare our results with existing experimental data and suggest new experiments.Comment: 4 pages, 1 figur

Influence of Generic Scale Invariance on Classical and Quantum 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 metal-superconductor 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.Comment: 55pp, 25 eps figs; final version, to appear in Rev Mod Phy

Breakdown of Landau-Ginzburg-Wilson theory for certain quantum phase transitions

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.Comment: 4 pp., REVTeX, no figs, final version as publishe

Superconductivity and Quantum Phase Transitions in Weak Itinerant Ferromagnets

It is argued 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 UGe_2. It is then 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 magnons to the longitudinal magnetic susceptibility. This qualitatively explains the phase diagram recently observed in UGe_2 and ZrZn_2.Comment: 10 pp., LaTeX, 5 ps figs., requires World Scientific style files (included), Invited contribution to MB1

Quantum critical behavior of clean itinerant ferromagnets

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 to unusual scaling behavior at the quantum critical point in 1 < d\leq 3, which we determine exactly. We also discuss the quantum-to-classical crossover at small but finite temperatures, which is characterized by the appearance of multiple temperature scales. A comparison with recent results on disordered itinerant ferromagnets is given.Comment: 13 pp., REVTeX, psfig, 3 eps figs, final version as publishe

The quantum phase transition of itinerant helimagnets

We investigate the quantum phase transition of itinerant electrons from a paramagnet to a state which displays long-period helical structures due to a Dzyaloshinskii instability of the ferromagnetic state. In particular, we study how the self-generated effective long-range interaction recently identified in itinerant quantum ferromagnets is cut-off by the helical ordering. We find that for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum phase transition is of second order with mean-field exponents. In contrast, for a weak Dzyaloshinskii instability the transition is analogous to that in itinerant quantum ferromagnets, i.e. it is of first order, as has been observed in MnSi.Comment: 5 pages RevTe

Percolation quantum phase transitions in diluted magnets

We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are different from the classical percolation values, but in two dimensions they can nonetheless be determined exactly. We develop a complete scaling theory of this transition, and we relate it to recent experiments in La$_{2}$Cu$_{1-p}$(Zn,Mg)$_{p}$O$_{4}$. Our results are also relevant for disordered interacting boson systems.Comment: 4 pages, 3 eps figures, final version, as publishe

Infinite randomness and quantum Griffiths effects in a classical system: the randomly layered Heisenberg magnet

We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the critical point has exotic infinite-randomness character. It is accompanied by strong power-law Griffiths singularities. We compute various thermodynamic observables paying particular attention to finite-size effects relevant for an experimental verification of our theory. We also study the critical dynamics within a Langevin equation approach and find it extremely slow. At the critical point, the autocorrelation function decays only logarithmically with time while it follows a nonuniversal power-law in the Griffiths phase.Comment: 10 pages, 2 eps figures included, final version as published