The study of critical phenomena and universal power laws has been one of the central advances in statistical mechanics during the second half of the past century, explaining traditional thermodynamic critical points 1 , avalanche behaviour near depinning transitions 2,3 and a wide variety of other phenomena 4 . Scaling, universality and the renormalization group claim to predict all behaviour at long length and timescales asymptotically close to critical points. In most cases, the comparison between theory and experiments has been limited to the evaluation of the critical exponents of the power-law distributions predicted at criticality. An excellent area for investigating scaling phenomena is provided by systems exhibiting crackling noise, such as the Barkhausen effect in ferromagnetic materials 5 . Here we go beyond powerlaw scaling and focus on the average functional form of the noise emitted by avalanches-the average temporal avalanche shape 4 . By analysing thin permalloy films and improving the data analysis methods, our experiments become quantitatively consistent with our calculation for the multivariable scaling function in the presence of a demagnetizing field and finite field-ramp rate.The average temporal avalanche shape has been measured for earthquakes 6 and for dislocation avalanches in plastically deformed metals 7,8 , but the primary experimental and theoretical focus has always been Barkhausen avalanches in magnetic systems 5,6,[9][10][11] . Theory and experiment agreed well for avalanche sizes and durations, but the strikingly asymmetric shapes found experimentally in ribbons 11 disagreed sharply with the theoretical predictions, for which the asymmetry in the scaling shapes under time reversal was at most very small 4,6 . (We note that the relevant models are not microscopically time-reversal invariant; temporal symmetry is thus emergent.) Doubts about universality 4 were resolved when eddy currents were shown to be responsible for the asymmetry, at least on short timescales 12 , but the exact form of the asymptotic universal scaling function of the Barkhausen avalanche shape still remained elusive.Here, we report an experimental study of Barkhausen noise in permalloy thin films, where a careful study of the average avalanche shapes leads to symmetric shapes, undistorted by eddy currents (which are suppressed by the sample geometry). We provide a quantitative explanation of the experimental results by solving exactly the mean-field theories for two general models of magnetic reversal: a domain-wall dynamics model 13 Time-series data (jagged line) are traditionally separated into avalanches using a threshold V th set above the instrumental noise (dotted blue line)-here breaking one avalanche into a few pieces. We instead do an optimal Wiener deconvolution (smoothed red curve, see text), allowing the use of a zero threshold (solid black line), which avoids distortions of the average shape and also gives more decades of size and duration scaling. Averaging over all avalanches with this duratio...

We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. The development of this model was motivated by recent observations of micron-sized critical fluctuations in plasma membrane vesicles that are detached from their cortical cytoskeleton. We incorporate criticality using a conserved order parameter Ising model coupled to a simple actin cytoskeleton interacting through point-like pinning sites. Using this minimal model, we recapitulate several experimental observations of plasma membrane raft heterogeneity. Small (r ∼ 20 nm) and dynamic fluctuations at physiological temperatures arise from criticality. Including connectivity to the cortical cytoskeleton disrupts large fluctuations, prevents macroscopic phase separation at low temperatures (T ≤ 22°C), and provides a template for long-lived fluctuations at physiological temperature (T = 37°C). Cytoskeleton-stabilized fluctuations produce significant barriers to the diffusion of some membrane components in a manner that is weakly dependent on the number of pinning sites and strongly dependent on criticality. More generally, we demonstrate that critical fluctuations provide a physical mechanism for organizing and spatially segregating membrane components by providing channels for interaction over large distances.

When external stresses in a system -physical, social or virtual -are relieved through impulsive events, it is natural to focus on the attributes of these avalanches . Here we report a thorough experimental investigation of slowly compressed Ni microcrystals, covering three orders of magnitude in nominal strain-rate, that exhibits unconventional quasi-periodic avalanche bursts and higher critical exponents as the strain rate is decreased. Our analytic and computational study naturally extends dislocation avalanche modeling 10,11 to incorporate dislocation relaxations and reveals the emergence of the self-organized avalanche oscillator, a novel critical state exhibiting oscillatory approaches toward a depinning critical point 12 . We demonstrate that the predictions of our theory are faithfully exhibited in our experiments.Physical systems under slowly increasing stress may respond through abrupt events. Such jumps in observable quantities are abundant, from complex social networks to earthquakes. Even though these avalanches appear randomly sized and placed, the statistical properties of avalanches are universal, falling into well understood non-equilibrium universality classes. The main unifying concept is the depinning of an 2 interface under an external field. An implicit assumption underlying these concepts is that all other coexisting physical processes are either too fast and thus average out, or too slow rendering a static approximation valid.However, the latter assumption is not always true if the slow processes rearrange the pinning landscape at rates comparable to the external field driving rates. For as the fast avalanches are scale invariant, the whole timeseries, including the waiting intervals between the fast events, is also scale invariant. It is there within the waiting intervals that a slow restructuring of the pinning field can thrive and alter universal predictions.While intermittent plastic flow is well known . However, most of these single crystal studies covered only a narrow range of nominal high strain rates. Preliminary evidence that suggests a more complex physical picture, was discussed by some of us in Ref. 16, where a rate dependence of the cumulative strain event size distributions was observed. Interesting rate effects have also been observed in materials with solute atoms, typically polycrystalline, that display the PLC phenomenon 17,18,19 . The PLC avalanche distribution exponents show no evidence of strain-rate dependence (albeit strain dependence), while PLC at lower rates turns into similar-size localized slip excitations and chaotic behavior 20 , distinctly different from the physical behavior observed in Ref. 16. Instead, the PLC avalanche behavior is more consistent with the phenomenology of theories of avalanches with weakening effects 21 . In our experiments, Ni microcrystals of comparatively large dimensions, having diameters between 18 and 30 µm, were uniaxially compressed 15 . By controlling the applied external stress to maintain a nominal strain rate and by detecting...

We study phase diagrams of a class of doped quantum dimer models on the square lattice with ground-state wave functions whose amplitudes have the form of the Gibbs weights of a classical doped dimer model. In this dimer model, parallel neighboring dimers have attractive interactions, whereas neighboring holes either do not interact or have a repulsive interaction. We investigate the behavior of this system via analytic methods and by Monte Carlo simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless transition from a quantum critical phase to a columnar phase. At low hole densities we find a dimer-hole liquid phase and a columnar phase, separated by a phase boundary which is a line of critical points with varying exponents. We demonstrate that this line ends at a multicritical point where the transition becomes first order and the system phase separates. The first-order transition coexistence curve is shown to become unstable with respect to more complex inhomogeneous phases in the presence of direct hole-hole interactions. We also use a variational approach to determine the spectrum of low-lying density fluctuations in the dimer-hole fluid phase.

We study inhomogeneous solutions of a 3+1-dimensional Einstein-Maxwell-scalar theory. Our results provide a holographic model of superconductivity in the presence of a charge density wave sourced by a modulated chemical potential. We find that below a critical temperature T c superconducting stripes develop. We show that they are thermodynamically favored over the normal state by computing the grand canonical potential. We investigate the dependence of T c on the modulation's wave vector, which characterizes the inhomogeneity. We find that it is qualitatively similar to that expected for a weakly coupled BCS theory, but we point out a quantitative difference. Finally, we use our solutions to compute the conductivity along the direction of the stripes.