Thursday 12th

Special session: 30 years of RFOT

I will attempt to frame the RFOT theory of Kirkpatrick, Thirumalai and Wolynes in the context of what was known in the 80's, emphasizing how much KTW anticipated, but also how some of their ideas needed to be reformulated or refined. Some open problems and prospective ideas will be discussed.
I describe how simulations with arbitrary real-number of replicas may be done. The 'droplet model' scenario suggests a transition line in the T-n diagram that is different from the one of the Parisi picture. Joint work with P.L. Contucci, F. Corberi, and E. Mingione.
Along the years, and especially in recent ones, it has been realised that self-induced disorder plays a key role in the physics of glasses. In this talk I will explain how self-induced disorder naturally comes about when considering fluctuations beyond the mean-field theory of the glass transition. I will discuss its main effects on the physical behavior of glasses, and the relationships that arise with the Random Field Ising model. I will focus in particular on yielding of amorphous solids under shear, and on thermodynamics at the glass transition.
Recently it has become clear (both experimentally and theoretically) that the ferromagnetic quantum phase transition in both clean and disordered metals is qualitatively modified by soft two-particle fermion excitations. In this talk I review these results and then argue that these same soft modes are crucial for understanding both the quantum SGT and the quantum SG phase in low temperature metals.

Pierfrancesco Urbani

Non-linear marginal stability and criticality in optimization problems

In many physical situations, marginal stability controls the properties of the final configurations obtained by local algorithms that optimize some cost function. In the simplest case where the energy landscape around such configurations admits an harmonic expansion, marginal stability corresponds to a gapless spectrum of harmonic excitations. In this talk I will instead focus on optimization problems for which the properties of the endpoint of gradient descent dynamics are described by non-linear excitations and marginal stability is encoded in a set of pseudogaps characterized by a set of critical exponents. I will show that the scaling theory emerging from replica symmetry breaking allows for the computation of such exponents. I will review this emerging scenario starting from spin glasses up to jamming of spheres and linear perceptron problems.
RFOT theory provides a detailed description of the structure and dynamics of supercooled liquids and glasses. Its mathematical foundation relies, however, on mean-field approximations that are difficult to control in finite dimensions, where a degree of phenomenology is often introduced. Computer simulations represent a key tool to probe the effects of finite dimensional fluctuations in simple glass-formers. I will show that combining numerical tools (such as parallel tempering, umbrella sampling and swap Monte Carlo) allows one to study many key quantities introduced within RFOT theory (point-to-set lengthscales, configurational entropy, Franz-Parisi free energy, surface tension exponent, lower critical dimension) in a temperature regime relevant to experiments.
The mosaic picture of supercooled liquids and glasses based on an underlying random first order transition provides a comprehensive framework for understanding a wide range of nonequilibrium phenomena. Twenty years ago, going beyond scaling analyses, an approximate molecular level theory was developed that rationalizes the concept of "fragility" in explaining the universal rules behind the chemical diversity of glassy dynamics. The success of the quantitative predictions of this theory for activation barriers, dynamical spatial correlations and the nonexponentiality of relaxation in supercooled liquids is reviewed. Within the glassy state, the theory has also predicted many surprising quantitative relationships between aging, rejuvenation and the mechanical behavior of glasses, including shear banding. The comparison of theoretical predictions with laboratory experiments will be highlighted.
A common characterization of the relation between energy landscape and slow dynamics in numerical studies of model glasses is provided by the study of inherent structures (IS). Given well-termalized configurations at some initial temperature, its IS is the energy minimum reached by a gradient descent algorithm. The study of inherent structures allows to define an onset temperature -higher than the estimated MCT temperature T_{MCT}- below which the landscape dominates the dynamics, and the IS energy depends on the initial temperature. Within mean-field theory, the simple spherical p-spin model predicts the existence of a unique 'threshold' energy value common to all the ISs corresponding to initial temperatures greater than the ergodicity breaking temperature T_{MCT}. The same is true if one considers a quench at some final temperature: the memory of the initial condition is lost by dynamics. In this talk I will show that this property, differently from the common belief, is not typical in mean-field, but depends on peculiar properties of the spherical p-spin. As soon as the model is modified - e.g. considering a mixture of p-spins - one finds a situation much closer to simulations of realistic systems. Integrating numerically the exact mean-field dynamical equations of the theory, one can identify an onset temperature T_{on}>T_{MCT} below which the IS energy depends on the initial temperature. I will discuss the features of the dynamics in this case and the theoretical puzzles it poses.
Within the big effort towards a theory of Glass formation, along the path traced by the Random First Order Transition theory, the uncovering of the Random Pinning Glass Transition represents a turning point that opened new perspectives on the possibility to approach and study the Ideal Glass Transition and the Ideal Glass itself. In this talk I will review its theoretical conception, developments and validations, opening the discussion on what has been achieved by its means and what is yet to be done.

Dave Thirumalai

From glass to super-diffusion in an evolving cell colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. By focusing on the early stages of tumor evolution in a minimal physical model, I will describe the collective cell dynamics in which mitosis and apoptosis play a critical role. Using simulations and theory I will show that tumor cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement of cells exhibits glassy behavior at times comparable to the cell cycle time, while undergoing super-diffusive behavior at times exceeding cell division times. A sketch of the theory for these characteristics motion will be given. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems.References:1) Abdul N Malmi-Kakkada, Xin Li, Himadri S. Samanta, Sumit Sinha, and D. Thirumalai, Phys. Rev. X 8: 021025 (2018).2) H. S. Samanta and D. Thirumalai, Phys. Rev. E 99: 032401 (2019).3) Abdul N Malmi-Kakkada, Xin Li, Sumit Sinha, and D. Thirumalai, biorxiv.org doi: https://doi.org/10.1101/683250
We develop a statistical mechanical approach based on the replica method to study the phase space of structure of a deep neural network. Specifically we analyze the configuration space of the synaptic weights in a feed-forward perceptron network of width N and depth L. By increasing strength of constraints, i.e., increasing the number M of imposed input/output patterns, successive glass transitions take place layer-by-layer starting next to the input/output boundaries going deeper into the bulk. For deep enough network the central part of the network remains in the liquid phase for finite strength of constraints. The successive glass transitions bring about a hierarchical free-energy landscape which evolves in space: it is most complex close to the boundaries but becomes renormalized into progressively simpler one in deeper layers. The character of free-energy landscape may provide clues to understand deep neural networks and related problems.