arXiv subjects

Tommaso Rizzo

Publications and source records attributed to Tommaso Rizzo.

At least 37 records · Page 2Linked to original sources

arXiv2022

From sub-aging to hyper-aging in structural glasses

We demonstrate non-equilibrium scaling laws for the aging dynamics in glass formers that emerge from combining a recent application of Onsager's theory of irreversible processes with the equilibrium scaling laws of glassy dynamics. Different scaling regimes are predicted for the evolution of the system's structural relaxation time $τ$ with age (waiting time $t_w$), depending on the depth of the quench from the liquid into the glass: \emph{simple aging} ($τ\sim t_w$) applies for quenches close to the critical point of mode-coupling theory (MCT) and implies \emph{sub-aging} ($τ\approx\ t_w^δ$ with $δ<1$) as a broad cross-over for quenches to nearly-arrested equilibrium states; \emph{hyper-aging} (or \emph{super-aging}, $τ\sim t_w^{δ'}$ with $δ'>1$) emerges for quenches deep into the glass. The latter is cut off by non-mean-field fluctuations that we account for within a recent extension of MCT, the stochastic $β$-relaxation theory (SBR). We exemplify the scaling laws by a schematic model that allows to quantitatively fit recent simulation results for density-quenched hard-sphere-like particles.

cond-mat.soft↗

arXiv2021

Correlation Functions of the Anharmonic Oscillator: Numerical Verification of Two-Loop Corrections to the Large-Order Behavior

Recently, the large-order behavior of correlation functions of the $O(N)$-anharmonic oscillator has been analyzed by us in [L. T. Giorgini et el., Phys. Rev. D 101, 125001 (2020)]. Two-loop corrections about the instanton configurations were obtained for the partition function, and the two-point and four-point functions, and the derivative of the two-point function at zero momentum transfer. Here, we attempt to verify the obtained analytic results against numerical calculations of higher-order coefficients for the $O(1)$, $O(2)$, and $O(3)$ oscillators, and demonstrate the drastic improvement of the agreement of the large-order asymptotic estimates and perturbation theory upon the inclusion of the two-loop corrections to the large-order behavior.

hep-th↗

arXiv2021

Path Integral Approach Unveils the Role of Complex Energy Landscape for Activated Dynamics of Glassy Systems

The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to compute the exponentially small probability of a jump from one metastable state to another. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical $p$-spin glass model that is invoked in diverse contexts from supercooled liquids to machine-learning algorithms. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.

cond-mat.dis-nn↗

arXiv2020

Solvable Models of Supercooled Liquids in Three Dimensions

We introduce a supercooled liquid model and obtain parameter-free quantitative predictions that are in excellent agreement with numerical simulations, notably in the hard low-temperature region characterized by strong deviations from Mode-Coupling-Theory behavior. The model is the Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional $M$-layer lattice. The agreement has implications beyond the specific model considered because the theory is potentially valid for many more systems, including realistic models and actual supercooled liquids.

cond-mat.dis-nn↗

arXiv2019

New loop expansion for the Random Magnetic Field Ising Ferromagnets at zero temperature

We apply to the Random Field Ising Model at zero temperature (T= 0) the perturbative loop expansion around the Bethe solution. A comparison with the standard epsilon-expansion is made, highlighting the key differences that make the new expansion much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T = 0 RG fixed point. This new loop expansion produces an effective theory with cubic vertices. We compute the one-loop corrections due to cubic vertices, finding new terms that are absent in the epsilon-expansion. However, these new terms are subdominant with respect to the standard, supersymmetric ones, therefore dimensional reduction is still valid at this order of the loop expansion.

cond-mat.dis-nn↗

arXiv2019

The fate of the bootstrap percolation hybrid critical point in finite dimension

Bootstrap, or $k$-core, percolation displays on the Bethe lattice a mixed first/second order phase transition with both a discontinuous order parameter and diverging critical fluctuations. I apply the recently introduced $M$-layer technique to study corrections to mean-field theory showing that at all orders in the loop expansion the problem is equivalent to a spinodal with quenched disorder. This implies that the mean-field hybrid transition does not survive in physical dimension. Nevertheless, its critical properties as an avoided transition, make it a proxy of the avoided Mode-Coupling-Theory critical point of supercooled liquids.

cond-mat.stat-mech↗

arXiv2018

Two-Loop Corrections to Large Order Behavior of $φ^4$ Theory

We consider the large order behavior of the perturbative expansion of the scalar $φ^4$ field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over $O(10^3)$ distinct eigenvalues determined numerically with the corresponding eigenfunctions.

cond-mat.stat-mech↗

arXiv2017

High Quality Queueing Information from Accelerated Active Network Tomography

Monitoring network state can be crucial in Future Internet infrastructures. Passive monitoring of all the routers is expensive and prohibitive. Storing, accessing and sharing the data is a technological challenge among networks with conflicting economic interests. Active monitoring methods can be attractive alternatives as they are free from most of these issues. Here we demonstrate that it is possible to improve the active network tomography methodology to such extent that the quality of the extracted link or router level delay is comparable to the passively measurable information. We show that the temporal precision of the measurements and the performance of the data analysis should be simultaneously improved to achieve this goal. In this paper we not only introduce a new efficient message-passing based algorithm but we also show that it is applicable for data collected by the ETOMIC high precision active measurement infrastructure. The measurements are conducted in the GEANT2 high speed academic network connecting the sites, which is an ideal test ground for such Future Internet applications.

cs.NI↗

arXiv2016

Dynamical Landau Theory of the Glass Crossover

I introduce a dynamical field theory to describe the glassy behavior in supercooled liquids. The mean-field approximation of the theory predicts a dynamical arrest transition, as in ideal Mode-Coupling-Theory and mean-field discontinuous Spin-Glass Models. Instead {\it beyond} the mean-field approximation the theory predicts that the transition is avoided and transformed into a crossover, as observed in experiments and simulations. To go beyond mean-field a standard perturbative loop expansion is performed at first. Approaching the ideal critical point this expansion is divergent at all orders and I show that the leading divergent term at any given order is the same of a dynamical stochastic equation, called Stochastic-Beta-Relaxation (SBR) in {\it EPL 106, 56003 (2014)}. At variance with the original theory SBR can be studied beyond mean-field directly, without the need to resort to a perturbative expansion. Thus it provides a qualitative and quantitative description of the dynamical crossover. For consistency reasons it is important to establish the connection between the dynamical field theory and SBR beyond perturbation theory. This can be done with the help of a stronger result: the dynamical field theory is {\it exactly} equivalent to a theory with quenched disorder. Qualitatively the non-perturbative mechanism leading to the crossover is therefore the same of SBR. Quantitatively SBR corresponds to make the mean-field approximation once the quenched disorder has been generated.

cond-mat.dis-nn↗

arXiv2015

Composite operators in Cubic Field Theories and Link Overlap Fluctuations in Spin-Glass Models

We present a complete characterization of the fluctuations and correlations of the squared overlap in the Edwards-Anderson Spin-Glass model in zero field. The analysis reveals that the energy-energy correlations (and thus the specific heat) have a different critical behavior than the fluctuations of the link overlap in spite of the fact that the average energy and average link overlap have the same critical properties. More precisely the link-overlap fluctuations are larger than the specific heat according to a computation at first order in the $6-ε$ expansion. An unexpected outcome is that the link-overlap fluctuations have a subdominant power-law contribution characterized by an anomalous logarithmic prefactor which is missing in the specific heat. In order to compute the $ε$ expansion we consider the problem of the renormalization of quadratic composite operators in a generic multicomponent cubic field theory: the results obtained have a range of applicability beyond spin-glass theory.

cond-mat.dis-nn↗

arXiv2015

The Glass Crossover from Mean-Field Spin-Glasses to Supercooled Liquids

Stochastic-Beta-Relaxation (SBR) provides a characterisation of the glass crossover in discontinuous Spin-Glasses and Supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling-Theory invoking a physical principle of time-scale invariance.

cond-mat.dis-nn↗

arXiv2015

On The Nature of the Glass Crossover

Stochastic Beta Relaxation (SBR) is a model for the dynamics of glass- forming liquids close to the glass transition singularity of the idealized mode- coupling theory (MCT) that has been derived from generic MCT-like theories by applying dynamical field-theory techniques. SBR displays a rich phenomenology common to most super-cooled liquids. 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 and the violation of the Stokes-Einstein relation between diffusion and viscosity. The solution of the model in three dimensions unveils a qualitative change at the crossover in the structure of dynamical fluctuations from a regime characterized by power-law increases of their amplitude and size to a regime dominated by strong Dynamical Heterogeneities: rare regions where dynamics is relatively much faster than in the rest of the system. While the relaxation time changes by orders of magnitude, the size of these regions does not change significantly and actually decreases below the crossover temperature. SBR cannot sustain too large fluctuations and could fail well below the crossover temperature. There it could be replaced by non-conventional activated dynamics characterized by elementary events with intrinsic time and length scales of an unusual large (but not necessarily increasing) size (mesoscopic vs. microscopic).

cond-mat.dis-nn↗

arXiv2015

Diluted Mean-Field Spin-Glass Models at Criticality

We present a method derived by cavity arguments to compute the spin-glass and higher-order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated to the existence of a non-zero solution of a homogeneous linear integral equation. Higher order susceptibilities, relevant for critical dynamics through the parameter exponent $λ$, can be expressed at criticality as integrals involving the critical eigenvector. The numerical evaluation of the corresponding analytic expressions is discussed. The method is illustrated in the context of the de Almeida-Thouless line for a spin-glass on a Bethe lattice but can be generalized straightforwardly to more complex situations.

cond-mat.dis-nn↗

arXiv2014

One-dimensional disordered Ising models by replica and cavity methods

Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor graph (p-spin) ensembles. We present exact analytical expressions, which can be efficiently approximated numerically, for many types of correlation functions and for the average free energies of open and closed finite chains. All the results achieved, with the exception of those involving closed chains, are then rigorously derived without replicas, using a probabilistic approach with the same flavour of cavity method.

cond-mat.dis-nn↗

arXiv2014

Finite size corrections to disordered Ising models on Random Regular Graphs

We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non self-intersecting loops in the graph, the weight being the free-energy shift due to the addition of the loop to an infinite tree.

cond-mat.dis-nn↗

arXiv2014

Anomalous finite size corrections in random field models

The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, to compute analytically the $O(\sqrt{1/N})$ finite size correction to the average free energy. We apply this method to two mean field Ising models, fully connected and random regular graphs, and compare the results to exact numerical algorithms. We argue that this behaviour is present in finite dimensional models as well.

cond-mat.dis-nn↗

arXiv2014

Qualitative Features at the Glass Crossover

We discuss some generic features of the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT). The analysis is based on a recent model by one of the authors for the intermediate-time dynamics ($β$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Combined with the assumption of time-temperature superposition for the slow structural ($α$) relaxation, the model naturally explains three 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, and two distinct growth regimes of the thermal susceptibility that has been associated to dynamical heterogeneities.

cond-mat.stat-mech↗

arXiv2014

Long-wavelength fluctuations lead to a model of the glass crossover

The effect of long wavelength fluctuations on the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $β$ regime is studied by means of the standard field-theoretical procedure for a genuine second-order phase transition. The resulting perturbative loop expansion can be resummed leading to an extension of the MCT equation for the critical correlator with local random fluctuations of the separation parameter. The corresponding model explains both qualitatively and quantitatively why the MCT dynamical singularity is transformed into a crossover from relaxational to activated dynamics. Dynamical Heterogeneities emerge naturally as the ergodicity-restoring mechanism instead of {\it ad hoc} hopping processes.

cond-mat.dis-nn↗