Critical Phenomena in Random
and Complex Systems

Abstracts

B Altshuler

Columbia University, New York, NY (USA)

Many-Body Localization, Ergodicity and Multi-fractality

Strictly speaking the laws of the conventional Statistical Physics, in particular the Equipartition Postulate, apply only in the presence of a thermostat. For a long time this restriction did not look crucial for most of the interesting systems - arbitrary weak coupling with the reservoir was believed to be sufficient. Recently there appeared two classes of quantum many-body systems with the coupling to the outside world that is (or is hoped to be) negligible: (1) cold quantum gases and (2) systems of qubits, which enjoy a continuous progress in their disentanglement from the environment. To describe such systems properly one should revisit the very foundations of the Statistical Mechanics. The first step in this direction was the development of the concept of Many-Body Localization (MBL) [1]: under certain conditions the states of a many-body system are localized in the Hilbert space resembling the celebrated Anderson Localization of single particle states in a random potential. There are reasons to believe that one-particle localization of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs (RRG) in many aspects is similar to a generic MBL. MBL implies that the state of the system decoupled from the thermostat depends on the initial conditions: the time averaging does not result in equipartition distribution, the entropy never reaches its thermodynamic value, and i.e. the ergodicity is violated. Variations of e.g. temperature can delocalize many body states. However, the recovery of the equipartition is not likely to follow the delocalization immediately: our numerical analysis of the RRG problem suggests that the extended states are multi-fractal at any finite disorder. Moreover, regular (no disorder!) Josephson junction arrays (JJA) under the conditions that are feasible to implement and control experimentally demonstrate both MBL and non-ergodic behavior [3].

[1] D. Basko, I. Aleiner, and B. Altshuler, Ann. Phys. 321, 1126 (2006).
[2] A. De Luca, B.L. Altshuler, V.E. Kravtsov, and A. Scardicchio, Phys. Rev. Lett. 113, 046806, (2014)
[3] Manuel Pino Garcia, L.B. Ioffe, and B.L. Altshuler, to be published

L Berthier

University of Montpellier (France)

Thermodynamic fluctuations in supercooled liquids

Theoretical approaches to the physics of glass-forming materials can be broadly organized in two categories, putting forward either a static (configurational entropy, geometrical motifs) or a dynamic (defects, dynamic facilitation) viewpoint. I will present results from computer simulations showing that viscous liquids approaching the glass transition develop non-trivial thermodynamic fluctuations which strongly correlate with the emergence of slow dynamics. A direct consequence of these findings is the possibility to induce equilibrium phase transitions by applying external fields to supercooled liquids, which are observed numerically in model liquids. A second consequence is a better definition of the configurational entropy, which should get us closer to testing the existence of an equilibrium phase transition underlying the formation of glassy states.

P Charbonneau

Duke University, Raleigh, NC (USA)

High-dimensional surprises near the glass and the jamming transitions

The structural glass problem is notoriously hard and controversial. Even at the mean-field level, there is little agreement about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. Contrasting entropic caging and force balance also suggests how one can embed jamming within the glass description. Through theory and simulation, we explicitly consider the role of spatial dimension, which allows us to explore the connection between rough free energy landscapes and mechanical marginality, as well as the role of geometry in the dynamical slowdown of colloid-like glass formers. We find that roughness brings about isostaticity and universal non-trivial critical exponents near jamming for the weak force distribution and the spatial spread of quasi-contacts. We also identify how hopping emerges from the structure of dense fluids and how it modifies the mean-field phenomenology in physically relevant dimensions.

E Corwin

University of Oregon, Eugene, OR (USA)

Jamming shapes up: geometry and energy landscape near the jamming transition

We examine both the real space and phase space geometry of packings below and above the jamming transition in GPU optimized simulations. Using geometric quantities derived from the Voronoi tessellation we report on a number of new geometric order parameters for jamming as well as the discovery of a new phase transition preceding the mechanical jamming transition. This phase transition corresponds to the appearance of a new kind of symmetry hidden in the shape of the Voronoi cells. We offer several possible routes towards renormalization of this system and discuss whether a field theory could be made to explain the various phases. We further explore the geometry of the very high dimensional phase space associated with a packing and report on direct measurements of the fractal nature of the energy landscape.

S Franz

Universite de Paris-Sud, Orsay (France)

Glassy Critical Points and the Random Field Ising Model

Research in recent years has emphasized the importance of fluctuations in understanding glassy phenomena in supercooled liquids. The present comprehension of long lived dynamical heterogeneities in these systems compares the growth of their typical size to the appearance of long range correlations at second order phase transition points. Unfortunately, in supercooled liquids, the theoretical study of these correlations beyond the mean field is just at an embryonic level. One of the difficulties lies in the fact that -with good physical reasons- the critical point corresponds to an unstable field theory. It turns out that one can cure the instability introducing appropriate physical constraints. In that case true critical points appear and they can be analyzed theoretically through the replica method. I will present the field theory of these critical points and show that the universality class of the Random Field Ising Model appears.

JP Garrahan

University of Notthingham (UK)

Dynamical Large Deviations and Glass Transitions

The dynamics of many-body systems is often richer than what one can infer simply from their statics. This dynamical richness is revealed by considering strictly dynamical observables. The full statistical characteristics of such quantities encode the dynamical properties of the system at hand. By considering their large deviations it is possible to derive a statistical mechanics of trajectories, which is to trajectories of the dynamics what equilibrium statistical mechanics is to configurations of the statics. In this talk I will describe this approach and how it can be applied to the glass transition problem. I will show how the underlying kinetic phenomenon of glass formation is related to a novel class of order-disorder transitions in trajectory, rather than configuration, space. I will consider the connection between the inactive dynamical phases this approach reveals and glasses prepared by more standard means. I will also discuss how these ideas extend to quantum systems.

F Guerra

Sapienza University, Rome (Italy)

Functional order parameters in disordered systems: the Legendre structure

We show the route to the establishment of the functional order parameters for the physical description of disordered systems. A complete scheme of dual Legendre variational principles is involved. The contrast with non-disordered systems is outlined. These considerations apply, in particular, to the Sherrington-Kirkpatrick model for spin glasses, to the Hopfield model for neural networks, to generalised multi-species models.

F Ladieu

CEA, Saclay (France)

New experimental results for the nonlinear responses of structural glasses

The introduction will be devoted to an overview of the third order responses measured in the last four years on supercooled liquids close to their glass transition temperature. It will be shown that these measurements can be interpreted as revealing the growing of a glassy correlation length when decreasing the temperature. Then, focusing on the role of a static electrical field, it will be shown that the associated nonlinear response reveals that a static electrical field slightly increases the glass transition temperature by an amount quadratic in the static electric field. Finally, the similarities and differences between these results for structural glasses and the corresponding ones for spin glasses will be discussed.

L Leuzzi

CNR/IPCF, Rome (Italy)

Spin-glass photonics: a statistical mechanical theory for lasing in random media

We present a unified approach to the theory of multimode laser cavities including an arbitrary amount of structural disorder. A general theory is studied for waves in optically active media with variable non-linearity and randomness. In the mean-field approximation phase diagrams can be devised in terms of optical power, degree of disorder and degree of openness of the cavity. In the thermodynamic limit of infinitely many modes the theory predicts four distinct regimes: a continuous wave behavior for low power, a standard mode-locking laser regime for high power and weak disorder, a random laser for high pumped power and large disorder and an intermediate regime of phase locking occurring in presence of disorder below the lasing threshold. For light-mode networks not straightforwardly reducible to mean-field theory and/or for finite systems a number of interesting phenomena can be studied applying statistical mechanical techniques, by means of numerical simulations and data analysis of experimental measurements. They range from the reproduction of mode-locked intensity spectra and ultra-short pulses in models for standard multimode lasers to the apparent onset of replica symmetry breaking in the intensity fluctuation overlap of some random laser compounds.

A Liu

University of Pennsylvania, Philadelphia, PA (USA)

Surfaces and Defects in Disordered Solids

One of the central features of the jamming transition is the existence of a boson peak frequency, ω*, marking the existence of a new class of vibrational modes beyond the usual sound modes. Here we consider the implication of these modes for free surfaces and flow defects. At free surfaces, we show that just as in the bulk, here is a new class of surface modes in addition to the usual surface plane waves [1]. We argue that these modes yield insight into the origin of the mobile layer observed at the surface of glassy films [1]. In the bulk, we use quasilocalized modes below ω* to identify flow defects, or particles vulnerable to rearrangement due to mechanical stress or temperature [2]. This is effective because, as in crystals, flow defects are particularly effective in scattering sound modes. Finally, we show that we can also identify flow defects from local structure alone, using machine learning methods [3]. We find that we can identify flow defects equally successfully in 2 and 3 dimensions, at temperatures ranging from well below to above the glass transition [3].

[1] D. M. Sussman, C. P. Goodrich, A. J. Liu and S. R. Nagel, to be published.
[2] M. L. Manning and A. J. Liu, Phys. Rev. Lett. 107, 108302 (2011).
[3] E. D. Cubuk, S. S. Schoenholz, J. M. Rieser, B. D. Malone, J. Rottler, D. J. Durian, E. Kaxiras and A. J. Liu, to be published.

V Martin Mayor

Universidad Complutense, Madrid (Spain)

Quantum versus Thermal annealing, the role of Temperature Chaos

The "D-Wave Two" machine presumably exploits quantum annealing effects to solve optimization problems. One of the preferred benchmarks is the search of ground-states for spin-glasses, one of the most computationally demanding problems in Physics. In fact, the "Janus" computer has been specifically built for spin-glasses simulations. Janus has allowed to extend the time scale of classical simulations by a factor of 1000. Whether D-wave's quantum annealing achieves a real speed-up as compared to the classical (thermal) annealing or not is a matter of investigation. Difficulties are twofold. On the one hand, the number of q-bits (503), although a World record, is still small. On the other hand, the 503 q-bits are disposed in a particular topology (the chimera lattice), where hard-to-solve instances are extremely rare for a small system. However, our work with Janus has taught us about a relevant physical effect: temperature chaos. Given a large enough number of q-bits, rough free-energy landscapes should be the rule, rather than the exception. Therefore, the meaningful question is: how well quantum-annealing performs in those instances displaying temperature-chaos? For a small number of q-bits, temperature-chaos is rare but fortunately not nonexistent. In the talk, we explain how our previous experience with Janus is allowing us to find chaotic instances for a small chimera lattice. The performance of both thermal annealing and quantum-annealing (D-wave) will be assessed over this set of samples.

S Nagel

University of Chicago, Chicago, IL (USA)

Relevance of jamming to understanding the mechanical properties of solids

For more than a century, physicists have described real solids in terms of perturbations about perfect crystalline order. Such an approach takes us only so far: a glass, another ubiquitous form of matter, cannot be described in any meaningful sense as a defected crystal. Even when completely rigid, glasses at low temperatures display many seemingly universal properties that are distinct from crystals. Is there a solid with complete disorder that serves as an opposite extreme to a crystal and which provides an alternative starting point for understanding materials? A solid created by jamming may constitute such a limit. Surprisingly, the same physics that determines the behavior at the jamming threshold also dominates the behavior of solids with surprisingly high order [1]. Moreover, the implications of jamming may be useful for understanding some of the characteristic structural, acoustic and thermodynamic properties of low-temperature glasses including the origin of the Boson peak [2] and the phonon echoes [3] that, up to now, have been interpreted as confirmation of the theory of quantum-mechanical two-level tunneling states.

[1] C.P. Goodrich, A.J. Liu, S. R. Nagel Nature Physics 10, 578 (2014)
[2] L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 95, 098301 (2005)
[3] J.C. Burton, S.R. Nagel, to be published.

P Nordblad

Uppsala University, Uppsala (Sweden)

Critical phenomena in spin glasses and other magnetic glasses

“Competing interaction in magnets: the root of ordered disorder or only frustration?” [P. Nordblad, Phys. Scr. 88 058301 (2013)] Results from ac- and dc- magnetization experiments on single crystalline FeMnTiO3, mono-dispersed densely packed maghemite nanoparticles and single crystalline La0.85Sr0.15CoO3 are used to exemplify magnetically disordered and frustrated systems entering glassy states at low temperatures; albeit, with vastly different nature of the interacting magnetic entities. These systems show critical dynamics with similar values of the dynamic exponent, zν. This indicates that paramagnetic, superparamagnetic and magnetic polaron(?) high temperature states all may be succeeded by a low temperature magnetic glass states. Is this phase transition scenario prevalent, or are many materials with reported low temperature glassy states better characterized by “only frustration”?

R Orbach

University of Texas, Austin, TX (USA)

Spin Glass Dynamics at the Mesoscale

The mesoscale allows a new probe of spin glass dynamics. Because the lower critical dimension for spin glasses dlow>2, the growth of the correlation length ξ(t,T) can change the nature of the spin glass state in real time. For samples of minimum characteristic length l, at times t such that ξ(t,T)<l (t< tco), conventional three dimensional dynamics are observed. When t> tco, there remain spin glass states for which ξ(t,T)≤l, in analogy with percolation theory. Activated dynamics are associated with these states, with activation energy proportional to ln(l/a0), where a0 is the average distance between spins. These dynamics control the time dependence of the zero field cooled and thermoremanent magnetization near the glass temperature Tg. They are also responsible for the frequency dependence of the dynamic susceptibility. Measurements on thin films of a-Ge:Mn and Cu:Mn and analyzed quantitatively within this framework.

G Parisi

Sapienza University, Rome (Italy)

Exact theory of dense amorphous hard spheres in high dimension

Mean field theory is usually valid when the number of dimensions goes to infinity. I will show that the statistical mechanics of hard spheres (neglecting crystallization) can be exactly computed in this limit. The glass transition is present and the scenario introduced by Kirkpatrick, Thirumalai, and Wolynes is correct. We find that at high density in the glass phase the simplest solution becomes unstable and a full replica symmetry breaking phase is present. The fullRSB solution predicts correctly that jammed packings are isostatic, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. These predictions compare very well with numerical results, in a nearly dimension independent way.

F Ricci Tersenghi

Sapienza University, Rome (Italy)

Steps to go beyond the Bethe approximation in disordered models: large deviations of critical correlations and loop corrections

In strongly disordered models, as spin glasses or random field models, although the mean field behavior has been roughly well understood, their finite dimensional physics is mainly studied by numerical simulation for the lack of a systematic and effective expansion below the upper critical dimension. With the aim of trying to follow a new expansion around the Bethe approximation, I will present some results which are preliminary steps for this expansion. On the one hand I will show how to obtain very detailed information, at the level of large deviations, about critical correlations. On the other hand I will show how to compute one-loop correction to the Bethe free-energy, which is equivalent to computing the leading term of the finite size corrections to models defined on random graphs.

T Rizzo

CNR/IPCF, Rome (Italy)

Qualitative Features of the Glass Crossover

Stochastic Beta Relaxation is a model for the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT) that I have derived by applying dynamical field-theory techniques to idealized MCT using the connection with Spin-Glass models. In its simplest version it naturally explains two prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time, the replacement of the Stokes-Einstein relation between diffusion and viscosity by a fractional law. The solution of the model in three dimensions displays a qualitative change in the dynamics across the crossover temperature from a regime where time and length scales have power-law increases to a regime characterized by both strong dynamical heterogeneities and a decreasing dynamical correlation length.

JJ Ruiz Lorenzo

Universidad de Extremadura, Badajoz (Spain)

The case for a three dimensional spin glass phase in presence of a magnetic field

The existence of a spin glass phase in presence of a magnetic field has been a long-debated and still open question from experiments, analytical approaches and numerical simulations. In this talk we will review the evidence, or lack thereof, for a phase transition in three dimensional spin glasses in a field by discussing some experiments and analytical results (mainly based in the renormalization group). In addition, we will show numerical simulations obtaining by different groups describing in detail our recent Janus results, firstly in four dimensions (static) and then our findings in three dimensions using dynamical (at equilibrium and out-of-equilibrium) and thermodynamic approaches.

G Szamel

Colorado State University, Ft Collins, CO (USA)

Long-range correlations in glasses and glassy fluids, and their connection to glasses' elasticity

In the first part of the talk I will show that the so-called dynamic glass transition implies the emergence of long-range density correlations. I will show that the long-range density correlations can be observed in computer simulations of glasses. Interestingly, very strong remnants of these correlations can be seen in simulations of glassy fluids. Next, I will turn to a simpler quantity, a correlation function of time-dependent transverse particle displacements. I will show that the long-range correlations of displacements are related to the plateau height of the stress-stress correlation function. Consequently, in the glass the shear modulus can be easily obtained from the correlations of transverse displacements. In the glassy fluid, the same correlation function provides information about transient viscoelastic response.

E Vincent

CEA, Saclay (France)

Superspin glass state in interacting magnetic nanoparticles

Interacting ferromagnetic nanoparticles in solid media (e.g. frozen ferrofluid) can undergo a transition from a superparamagnetic to a glassy state at low temperature. The glassy state formed by the “superspins” born by the nanoparticles is termed “superspin glass” (SSG). It can exhibit the same phenomenology as atomic spin glasses : critical behavior at the transition, slow dynamics, aging, memory effects, etc. The characteristic time scale for flipping a superspin is ~10-9 s in the superparamagnetic phase (to be compared with ~10-12 s for paramagnetic spins), and much longer at lower temperatures, due to freezing by the individual anisotropy energy barriers of the nanoparticles. Hence, the SSG dynamics takes place between the experimental time scale of spin glasses and that of numerical simulations. We have investigated how the SSG dynamics of a frozen ferrofluid is affected by “texturation” (alignment of the anisotropy axes of the nanoparticles by applying a magnetic field in the liquid phase) [1,2]. Via magnetization relaxation experiments at low temperatures, we were able to estimate the superspin correlation length for both textured and non-textured samples. The comparison with simulations and experiments on atomic spin glasses shows that the dynamic correlations in the SSG appear to develop in a way reminiscent to those in atomic spin glasses at intermediate time/length scales.

[1] S. Nakamae, C. Crauste-Thibierge, K. Komatsu, D. L’Hôte, E. Vincent, E. Dubois, V. Dupuis and R. Perzynski, Journal of Physics D : Applied Physics 43, 474001 (2010).
[2]S. Nakamae, C. Crauste-Thibiere, D. L’Hôte, E. Vincent, E. Dubois, V. Dupuis and R. Perzynski, Applied Physics Letters 101, 242409 (2012).

H Yoshino

Osaka University, Osaka (Japan)

Twisting and breaking glasses: a replica approach

Glasses are frozen liquids. In this talk we discuss recent progress of a microscopic theoretical approach on the mechanical properties of glasses which combines the liquid theory and the replica method [1-4]. We predict that replica symmetry breaking implies a hierarchy of rigidities which may be accessible experimentally especially around the jamming point [3].

[1] H. Yoshino and M. Mezard, Phys. Rev. Lett. 105, 015504 (2010).
[2] Y. Yoshino, J. Chem. Phys. 136, 214108 (2012).
[3] H. Yoshino and F. Zamponi, arXiv:1403.6967.
[4] C. Rainone, P. Urbani, H. Yoshino and F. Zamponi, in preparation.

P Young

UC Santa Cruz, Santa Cruz, CA (USA)

Spin glasses in a magnetic field

A surprising property of the infinite-range spin glass proposed by Sherrington and Kirkpatrick (SK) is a line of transitions in a magnetic field first found by de Almeida and Thouless (AT line). The surprise is that this transition occurs without symmetry breaking (of the spins). Whether the AT line occurs in real, e.g. 3-dimensional, spin glasses is a major unsolved question. If real spin glasses are qualitatively similar to the Parisi solution of the SK model, then, by definition, it does occur. This so-called "replica symmetry breaking" (RSB) scenario for the spin glass state below the transition temperature Tc, is in contrast to the "droplet picture", proposed in greatest detail by Fisher and Huse, in which there is no AT line. We have studied this question using large-scale numerical simulations for short-range models and, in greater detail, for long-range models with power-law interactions, which are argued to be similar to short-range models in a range of dimensions. Using standard finite-size scaling (FSS) we do not find an AT line, at least below six dimensions. However, a modified FSS proposed by Leuzzi et al the situation seems to imply an AT line in four dimensions (in contrast to standard FSS) but we do not find strong evidence for an AT line in three dimensions even with modified FSS. A better understanding of corrections to FSS in spin glasses in a magnetic field is needed to conclude definitively whether or not there is an AT line in three dimensions. (Work in collaboration with Helmut Katzgraber, Mike Moore, and Derek Larson)


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