Browsing by Subject "cond-mat.stat-mech"

Now showing 1 - 20 of 31

Metadata only
A nontrivial critical fixed point for replica-symmetry-breaking transitions
(2017-04-01) Charbonneau, Patrick; Yaida, Sho
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon--the Gardner transition--has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_u=6. Here, we obtain evidence for the existence of these transitions in d
Open Access
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
(2017-04-23) Liu, JG; Lu, J; Margetis, D; Marzuola, JL
In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the weighted-$H^{-1}$ (nonlinear) gradient flow of a convex, singular surface free energy in homoepitaxy. The PDE is motivated both by an atomistic broken-bond model and a mesoscale model for steps. By constructing an explicit solution to the PDE, we demonstrate the lack of symmetry in the evolution of top and bottom facets in periodic surface profiles. Our explicit, analytical solution is compared to numerical simulations of the PDE via a regularized surface free energy.
Open Access
Bayesian reconstruction of memories stored in neural networks from their connectivity
Goldt, Sebastian; Krzakala, Florent; Zdeborová, Lenka; Brunel, Nicolas
The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models and explore the limitations of reconstructing stored patterns from synaptic connectivity.
Open Access
Breaking the glass ceiling: Configurational entropy measurements in extremely supercooled liquids
(2017-06-01) Berthier, Ludovic; Charbonneau, Patrick; Coslovich, Daniele; Ninarello, Andrea; Ozawa, M; Yaida, Sho
Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is found also in simulations even beyond the experimental glass transition. Our numerical results thus open a new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.
Open Access
Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions
Berthier, Ludovic; Charbonneau, Patrick; Kundu, Joyjit
The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse mixtures fully bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions $d=2$ and $3$. Here, we consider suitably optimized systems in $d=2, 3,\dots, 8$, to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains finite in the limit $d \to \infty$. This shows that the glassy dynamics in high dimensions $d>3$ is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.
Open Access
Characterization and efficient Monte Carlo sampling of disordered microphases.
(The Journal of chemical physics, 2021-06) Zheng, Mingyuan; Charbonneau, Patrick
The disordered microphases that develop in the high-temperature phase of systems with competing short-range attractive and long-range repulsive (SALR) interactions result in a rich array of distinct morphologies, such as cluster, void cluster, and percolated (gel-like) fluids. These different structural regimes exhibit complex relaxation dynamics with marked heterogeneity and slowdown. The overall relationship between these structures and configurational sampling schemes, however, remains largely uncharted. Here, the disordered microphases of a schematic SALR model are thoroughly characterized, and structural relaxation functions adapted to each regime are devised. The sampling efficiency of various advanced Monte Carlo sampling schemes-Virtual-Move (VMMC), Aggregation-Volume-Bias (AVBMC), and Event-Chain (ECMC)-is then assessed. A combination of VMMC and AVBMC is found to be computationally most efficient for cluster fluids and ECMC to become relatively more efficient as density increases. These results offer a complete description of the equilibrium disordered phase of a simple microphase former as well as dynamical benchmarks for other sampling schemes.
Open Access
Coherence distillation machines are impossible in quantum thermodynamics
(Nature Communications, 2020-12) Marvian, Iman
The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence a "coherence distillation machine", i.e. a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This question is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can we distill synchronized clocks in pure states, at a non-zero rate? In this paper we study quantities called "coherence cost" and "distillable coherence", which determine the rate of conversion of coherence in a standard pure state to general mixed states, and vice versa, in the context of quantum thermodynamics. We find that the coherence cost of any state (pure or mixed) is determined by its Quantum Fisher Information (QFI), thereby revealing a novel operational interpretation of this central quantity of quantum metrology. On the other hand, we show that, surprisingly, distillable coherence is zero for typical (full-rank) mixed states. Hence, we establish the impossibility of coherence distillation machines in quantum thermodynamics, which can be compared with the impossibility of perpetual motion machines or cloning machines. To establish this result, we introduce a new additive quantifier of coherence, called the "purity of coherence", and argue that its relation with QFI is analogous to the relation between the free and total energies in thermodynamics.
Open Access
Comment on "kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system"
(Physical Review Research, 2021-09-01) Hu, Y; Charbonneau, P
Huerta [Phys. Rev. Research 2, 033351 (2020)2643-156410.1103/PhysRevResearch.2.033351] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a Kosterlitz-Thouless (KT)-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional system, however, contradicts long-held physical expectations. To clarify if the proposed ordering persists in the thermodynamic limit, we introduce an exact transfer matrix approach to expeditiously generate configurations of very large subsystems that are typical of equilibrium thermodynamic (infinite-size) systems. The power-law decay of positional order is found to extend only over finite distances. We conclude that the numerical simulation results reported are associated with a crossover unrelated to KT-type physics, and not with a proper thermodynamic phase transition.
Open Access
Correlation lengths in quasi-one-dimensional systems via transfer matrices
(Molecular Physics, 2018-06) Hu, Y; Fu, L; Charbonneau, P
© 2018 Informa UK Limited, trading as Taylor & Francis Group. Using transfer matrices up to next-nearest-neighbour interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers [Fu et al., Soft Matter 13, 3296 (2017)]. Here, we identify the theoretical basis for these behaviours. In particular, we associate kinks in the growth of correlation lengths with eigenvalue crossing and splitting. Understanding the origin of such structural crossovers answers questions raised by earlier studies, and thus bridges the gap between theory and simulations for these reference models.
Open Access
Dynamics around the Site Percolation Threshold on High-Dimensional Hypercubic Lattices
Biroli, Giulio; Charbonneau, Patrick; Hu, Yi
Recent advances on the glass problem motivate reexamining classical models of percolation. Here, we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical dimension of simple percolation, d_u=6. Using theory and simulations, we consider the scaling regime part, and obtain that both caging and subdiffusion scale logarithmically for d >= d_u. The theoretical derivation considers Bethe lattices with generalized connectivity and a random graph model, and employs a scaling analysis to confirm that logarithmic scalings should persist in the infinite dimension limit. The computational validation employs accelerated random walk simulations with a transfer-matrix description of diffusion to evaluate directly the dynamical critical exponents below d_u as well as their logarithmic scaling above d_u. Our numerical results improve various earlier estimates and are fully consistent with our theoretical predictions.
Open Access
Finite Dimensional Vestige of Spinodal Criticality above the Dynamical Glass Transition.
(Physical review letters, 2020-09) Berthier, Ludovic; Charbonneau, Patrick; Kundu, Joyjit
Finite dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalize configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from d=3 to d=10. We observe a strong softening of the mean-field square-root singularity in d=3 that is progressively restored as d increases above d=8, in surprisingly good agreement with perturbation theory.
Open Access
Finite-size effects in the microscopic critical properties of jammed configurations: A comprehensive study of the effects of different types of disorder.
(Physical review. E, 2021-07) Charbonneau, Patrick; Corwin, Eric I; Dennis, R Cameron; Díaz Hernández Rojas, Rafael; Ikeda, Harukuni; Parisi, Giorgio; Ricci-Tersenghi, Federico
Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces (f) and gaps (h) are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, d→∞ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, d=2 and 3. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of f and h for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of h than in that of f. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both f and h. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations.
Open Access
High-dimensional percolation criticality and hints of mean-field-like caging of the random Lorentz gas.
(Physical review. E, 2021-08) Charbonneau, Benoit; Charbonneau, Patrick; Hu, Yi; Yang, Zhen
The random Lorentz gas (RLG) is a minimal model for transport in disordered media. Despite the broad relevance of the model, theoretical grasp over its properties remains weak. For instance, the scaling with dimension d of its localization transition at the void percolation threshold is not well controlled analytically nor computationally. A recent study [Biroli et al., Phys. Rev. E 103, L030104 (2021)2470-004510.1103/PhysRevE.103.L030104] of the caging behavior of the RLG motivated by the mean-field theory of glasses has uncovered physical inconsistencies in that scaling that heighten the need for guidance. Here we first extend analytical expectations for asymptotic high-d bounds on the void percolation threshold and then computationally evaluate both the threshold and its criticality in various d. In high-d systems, we observe that the standard percolation physics is complemented by a dynamical slowdown of the tracer dynamics reminiscent of mean-field caging. A simple modification of the RLG is found to bring the interplay between percolation and mean-field-like caging down to d=3.
Open Access
Interplay between percolation and glassiness in the random Lorentz gas.
(Physical review. E, 2021-03) Biroli, Giulio; Charbonneau, Patrick; Corwin, Eric I; Hu, Yi; Ikeda, Harukuni; Szamel, Grzegorz; Zamponi, Francesco
The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits a continuous localization transition controlled by void space percolation. The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. In order to clarify the interplay between the seemingly incompatible percolation and caging descriptions of the RLG, we consider its exact mean-field solution in the infinite-dimensional d→∞ limit and perform numerics in d=2...20. We find that for sufficiently high d the mean-field caging transition precedes and prevents the percolation transition, which only happens on timescales diverging with d. We further show that activated processes related to rare cage escapes destroy the glass transition in finite dimensions, leading to a rich interplay between glassiness and percolation physics. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of particle hopping in structural glasses.
Open Access
Lecture Notes on the Statistical Mechanics of Disordered Systems
(2017-08-23) Charbonneau, Patrick
This material complements David Chandler's Introduction to Modern Statistical Mechanics (Oxford University Press, 1987) in a graduate-level, one-semester course I teach in the Department of Chemistry at Duke University. Students enter this course with some knowledge of statistical thermodynamics and quantum mechanics, usually acquired from undergraduate physical chemistry at the level of D. A. McQuarrie & J. D. Simon's Physical Chemistry: A Molecular Approach (University Science Books, 1997). These notes, which introduce students to a modern treatment of glassiness and to the replica method, build on the material and problems contained in the eight chapters of Chandler's textbook.
Open Access
Lyapunov exponent and susceptibility
(2017-08-23) Charbonneau, Patrick; Li, Yue Cathy; Pfister, Henry D; Yaida, Sho
Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with imperfect measurement of the initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical zeta function. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the zeta function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance, and is tested against Monte Carlo simulations.
Open Access
Mean-Field Caging in a Random Lorentz Gas.
(The journal of physical chemistry. B, 2021-06-07) Biroli, Giulio; Charbonneau, Patrick; Hu, Yi; Ikeda, Harukuni; Szamel, Grzegorz; Zamponi, Francesco
The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, d → ∞ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that, as d increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite-d perturbative and nonperturbative (instantonic) corrections [Biroli et al. Phys. Rev. E 2021, 103, L030104]. Here, we expand on the d → ∞ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the 1/d correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that, although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the d → ∞ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.
Open Access
Memory Formation in Jammed Hard Spheres.
(Physical review letters, 2021-02) Charbonneau, Patrick; Morse, Peter K
Liquids equilibrated below an onset condition share similar inherent states, while those above that onset have inherent states that markedly differ. Although this type of materials memory was first reported in simulations over 20 years ago, its physical origin remains controversial. Its absence from mean-field descriptions, in particular, has long cast doubt on its thermodynamic relevance. Motivated by a recent theoretical proposal, we reassess the onset phenomenology in simulations using a fast hard sphere jamming algorithm and find it to be both thermodynamically and dimensionally robust. Remarkably, we also uncover a second type of memory associated with a Gardner-like regime of the jamming algorithm.
Open Access
Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
Charbonneau, Patrick; Hu, Yi; Raju, Archishman; Sethna, James P; Yaida, Sho
A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point but, given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point/limit cycle may thus stay finite for all dimensions.
Open Access
Non-local SPDE limits of spatially-correlated-noise driven spin systems derived to sample a canonical distribution
Gao, Yuan; Marzuola, Jeremy L; Mattingly, Jonathan C; Newhall, Katherine A
We study the macroscopic behavior of a stochastic spin ensemble driven by a discrete Markov jump process motivated by the Metropolis-Hastings algorithm where the proposal is made with spatially correlated (colored) noise, and hence fails to be symmetric. However, we demonstrate a scenario where the failure of proposal symmetry is a higher order effect. Hence, from these microscopic dynamics we derive as a limit as the proposal size goes to zero and the number of spins to infinity, a non-local stochastic version of the harmonic map heat flow (or overdamped Landau-Lipshitz equation). The equation is both mathematically well-posed and samples the canonical/Gibbs distribution related to the kinetic energy. The failure of proposal symmetry due to interaction between the confining geometry of the spin system and the colored noise is in contrast to the uncorrelated, white-noise, driven system. Specifically, the choice of projection of the noise to conserve the magnitude of the spins is crucial to maintaining the proper equilibrium distribution. Numerical simulations are included to verify convergence properties and demonstrate the dynamics.