1,018 research outputs found
Real space renormalization group theory of disordered models of glasses
No full textWe develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition
Spin glass in a field: A new zero-temperature fixed point in finite dimensions
No full textBy using real-space renormalization group (RG) methods, we show that spin glasses in a field display a
new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase
are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical
exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass
phase we discovered has unusual properties, which are intermediate between the ones conjectured by
droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-
standing debate about the behavior of spin glasses in a field
Super-Potts glass: A disordered model for glass-forming liquids
No full textWe introduce a disordered system, the super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pairwise interactions. Its exact solution on a completely connected lattice demonstrates that, for large enough M, it belongs to the class of mean-field systems solved by a one-step replica symmetry breaking ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behavior similar to the one of glass-forming liquids. The super-Potts glass is therefore a disordered model allowing one to perform extensive and detailed studies of the random first-order transition in finite dimensions. We also discuss its behavior for small values of M, which is similar to the one of spin glasses in a field
Aging and relaxation near random pinning glass transitions
No full textPinning particles at random in supercooled liquids is a promising route to make substantial progress in the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in the presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual mode coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c-T phase diagram delimited by those two lines leads to aging. By extending our results to finite dimensional systems we predict non-interrupted aging only for quenches on the ideal glass transition line and two very different types of equilibrium relaxations for quenches below and above it
Patch-repetition correlation length in glassy systems
No full textWe obtain the patch-repetition entropy Σ within the Random First-Order Transition (RFOT) theory and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size ℓ, Σ(ℓ), scales as scℓd+Aℓd− 1 down to length scales of the order of one, where A is a positive constant, sc is the configurational entropy density and d the spatial dimension. As a consequence, the only meaningful length that can be defined from patch-repetition is the crossover length ξ=A/sc. We relate ξ to the typical length scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, into the possible real-space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size
Random pinning glass transition: Hallmarks, mean-field theory and renormalization group analysis
No full textFine morphology of the myrmecophilous larva of Paussus kannegieteri (Coleoptera: Carabidae: Paussinae: Paussini). Corresponding author
No full textFIGURES 13–18. Paussus kannegieteri third instar larva: 13, thorax, left lateral view; 14, thorax, dorsal view; 15, mesothoracic spiracle; 16, metathoracic spiracle-like structure; 17, mesothoracic leg, anterolateral view; 18, apex of metathoracic leg with lanceolate setae, posterolateral view. CO = coxa, ls = lanceolate setae, m = membrane, ME = mesonotum, MT = metanotum, pe = peritreme, PR = pronotum, un = claw. Scale bars: Figs. 13–14 = 500 µm; Fig. 15 = 10 µm; Fig. 16 = 20 µm; Fig. 17 = 200 µm; Fig. 18 = 50 µm.Published as part of Giulio, Andrea Di, 2008, Fine morphology of the myrmecophilous larva of Paussus kannegieteri (Coleoptera: Carabidae: Paussinae: Paussini), pp. 37-50 in Zootaxa 1741 on page 44, DOI: 10.5281/zenodo.18152
Non-perturbative renormalization group :from equilibrium to non-equilibrium
No full textExaminateur: Daniel Ariosa, Giulio Biroli, Leticia Cugliandolo.Rapporteur: Frédéric van Wijland, Holger Gies
Who is afraid of big bad minima? Analysis of gradient-flow in spiked matrix-tensor models
No full textGradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a quantitative theory explaining this behaviour in a spiked matrix-tensor model. Our framework is based on the Kac-Rice analysis of stationary points and a closed-form analysis of gradient-flow originating from statistical physics. We show that there is a well defined region of parameters where the gradient-flow algorithm finds a good global minimum despite the presence of exponentially many spurious local minima. We show that this is achieved by surfing on saddles that have strong negative direction towards the global minima, a phenomenon that is connected to a BBP-type threshold in the Hessian describing the critical points of the landscapes
- …
