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

On \epsilon-conjecture in a-theorem

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the \epsilon-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimension. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories.Comment: 5 pages, v2: clarifications added to emphasize that we have no intention of invalidating the derivation by Komargodski and Schwimmer when the renormalization group flow is between two conformal field theorie

Deformations of Lifshitz holography

The simplest gravity duals for quantum critical theories with z=2 `Lifshitz' scale invariance admit a marginally relevant deformation. Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Lambda as well as finite temperature T. We describe the thermodynamics of these black holes in the quantum critical regime where T >> Lambda^2. The deformation changes the asymptotics of the spacetime mildly and leads to intricate UV sensitivities of the theory which we control perturbatively in Lambda^2/T.Comment: 1+27 pages, 12 figure

Is local scale invariance a generic property of ageing phenomena ?

In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J. Phys. A 37, 10479] it is shown that the critical autoresponse function of the 1+1-dimensional contact process is not in agreement with the predictions of local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques

Probing the Planck Scale with Neutrino Oscillations

Quantum gravity "foam", among its various generic Lorentz non-invariant effects, would cause neutrino mixing. It is shown here that, if the foam is manifested as a nonrenormalizable effect at scale M, the oscillation length generically decreases with energy $E$ as (E/M)^(-2). Neutrino observatories and long-baseline experiments should have therefore already observed foam-induced oscillations, even if M is as high as the Planck energy scale. The null results, which can be further strengthened by better analysis of current data and future experiments, can be taken as experimental evidence that Lorentz invariance is fully preserved at the Planck scale, as is the case in critical string theory.Comment: 11 pages, 2 figures. Final version published in PRD. 1 figure, references, clarifications and explanations added. Results unchange

Multi-scale Orderless Pooling of Deep Convolutional Activation Features

Deep convolutional neural networks (CNN) have shown their promise as a universal representation for recognition. However, global CNN activations lack geometric invariance, which limits their robustness for classification and matching of highly variable scenes. To improve the invariance of CNN activations without degrading their discriminative power, this paper presents a simple but effective scheme called multi-scale orderless pooling (MOP-CNN). This scheme extracts CNN activations for local patches at multiple scale levels, performs orderless VLAD pooling of these activations at each level separately, and concatenates the result. The resulting MOP-CNN representation can be used as a generic feature for either supervised or unsupervised recognition tasks, from image classification to instance-level retrieval; it consistently outperforms global CNN activations without requiring any joint training of prediction layers for a particular target dataset. In absolute terms, it achieves state-of-the-art results on the challenging SUN397 and MIT Indoor Scenes classification datasets, and competitive results on ILSVRC2012/2013 classification and INRIA Holidays retrieval datasets