Criticality and quenched disorder: rare regions vs. Harris criterion

We employ scaling arguments and optimal fluctuation theory to establish a general relation between quantum Griffiths singularities and the Harris criterion for quantum phase transitions in disordered systems. If a clean critical point violates the Harris criterion, it is destabilized by weak disorder. At the same time, the Griffiths dynamical exponent $z'$ diverges upon approaching the transition, suggesting unconventional critical behavior. In contrast, if the Harris criterion is fulfilled, power-law Griffiths singularities can coexist with clean critical behavior but $z'$ saturates at a finite value. We present applications of our theory to a variety of systems including quantum spin chains, classical reaction-diffusion systems and metallic magnets; and we discuss modifications for transitions above the upper critical dimension. Based on these results we propose a unified classification of phase transitions in disordered systems.Comment: 4.5 pages, 1 eps figure, final version as publishe

Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of temporal disorder on nonequilibrium processes. We also discuss how general this exotic critical behavior is, we illustrate the results by computer simulations, and we touch upon experimental applications of our theory.Comment: 6 pages (including 3 eps figures). Final version as publishe

The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity

This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain `superselection laws' that arise in current applications of these techniques to solving the diffeomorphism constraint are considered. Their status is elucidated by studying an analogous system: 2+1 Euclidean gravity. For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as `Refined Algebraic Quantization.'Comment: Latex, 14 pages, to appear in Journ. Math. Phy

Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent $z'$ saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion which implies that weak disorder is renormalization-group irrelevant and the rare-region classification which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte-Carlo simulations of systems with up to $70^5$ sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. {\bf 112}, 075702 (2014)], and we discuss implications for other phase transitions.Comment: 10 pages, 5 eps figures included, applies the optimal fluctuation theory of arXiv:1309.0753 to the contact proces

Local defect in a magnet with long-range interactions

We investigate a single defect coupling to the square of the order parameter in a nearly critical magnet with long-range spatial interactions of the form $r^{-(d+\sigma)}$, focusing on magnetic droplets nucleated at the defect while the bulk system is in the paramagnetic phase. Because of the long-range interaction, the droplet develops a power-law tail which is energetically unfavorable. However, as long as $\sigma>0$, the tail contribution to the droplet free energy is subleading in the limit of large droplets; and the free energy becomes identical to the case of short-range interactions. We also study the droplet quantum dynamics with and without dissipation; and we discuss the consequences of our results for defects in itinerant quantum ferromagnets.Comment: 8 pages, 5 eps figures, final version, as publishe

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the $N$-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail, and we discuss broader implications for the fate of first-order quantum phase transitions in disordered systems.Comment: 5 pages, 4 figure

Trade and the Competitiveness Agenda

The global economic crisis has forced a major rethinking of the respective roles of governments and markets in the processes of trade and growth. Indeed, industrial policy seems to be back in fashion—or, at least, talking about it is. But a renewed “activism” by government in the trade and growth agenda need not mean a return to old-style policies of import substitution and “picking winners.” Instead, it may mean a stronger focus on competitiveness by unlocking the constraints to private sector–led growth. This note discusses the renewed role of government in trade and growth policy from the competitiveness angle, and it suggests some priorities for the new competitiveness agenda.trade, competitiveness, financial crisis, growth, industrial policy, import substitution, picking winners, trade policy, exports, imports

The use of derivatives in the Spanish mutual fund industry

We study the use of derivatives in the Spanish mutual fund industry. The picture that emerges from our analysis is rather negative. In general, the use of derivatives does not improve the performance of the funds. In only one out of eight categories we find some (very weak and not robust) evidence of superior performance. In most of the cases users significantly underperform non users. Furthermore, users do not seem to exhibit superior timing or selectivity skills either, but rather the contrary. This bad performance is only partially explained by the larger fees funds using derivatives charge. Moreover, we do not find evidence of derivatives being used for hedging purposes. We do find evidence of derivatives being used for speculation. But users in only one category exhibit skills as speculators. Finally, we find evidence of derivatives being used to manage the funds’ cash inflows and outflows more efficiently.Mutual Funds, Derivative use, Risk Management