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Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation probability of a site depends on the state of its neighbours through a certain threshold parameter. In this paper we investigate the phase behavior of the bootstrap percolation on the regular random graph in the limit in which the threshold parameter and lattice connectivity become both increasingly large while their ratio $\alpha$ is held constant. We find that the mixed phase behavior is preserved in this limit, and that multiple transitions and higher-order bifurcation singularities occur when $\alpha$ becomes a random variable., Comment: 6 pages, 4 figures

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter-Mellinck regime of turbulent superfluids, are extended to describe the transition to ballistic regime in narrow channels wherein the radius $R$ is comparable to (or smaller than) the phonon mean-free path $\ell$ in superfluid helium. To do so we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to $R^2$ (Landau regime) to another one proportional to $R\ell$ (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates., Comment: 16 pages

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F12 schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields new predictions for dynamic relaxation exponents below an upper critical dimension of 6.

We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits reentrancy of the liquid-glass transition line, two distinct glass states and a glass-to-glass transition, much similar to what has been previously obtained by Mode-Coupling Theory, numerical simulations and experiments. The presence of the phase reentrance implies that for a suitable choice of the intensity and attraction range, high-density sphere packings more compact than the one corresponding to pure hard-spheres can be constructed in polynomial time in the number of particles (at fixed, large d) for packing fractions smaller than 6.5 d 2^{-d}. Although our derivation is not a formal mathematical proof, we believe it meets the standards of rigor of theoretical physics, and at this level of rigor it provides a small improvement of the lower bound on the sphere packing problem., Comment: 18 pages, 7 figures -- Proceedings of the International Meeting on "Inference, Computation, and Spin Glasses", Sapporo, Japan, July 28-30, 2013

The phase behavior of hard-sphere particles interacting with a short-ranged potential is studied in the limit of infinite space dimensionality via the Franz-Parisi approach and the replica method of disordered systems. For an attractive square-well potential the phase diagram exhibits reentrancy of the liquid-glass transition, multiple glass states and glass-glass transition. For a repulsive square shoulder potential no such special features are observed. Our results show that the Franz-Parisi approach can be consistently extended to deal with higher-order glass singularities and that interparticle attraction is crucial for complex glassy behavior in large enough dimensions, at least for monodisperse systems., Comment: 5 pages, 6 figures

It has been recently established that heterogeneous bootstrap percolation and related dynamic facilitation models exhibit a complex hierarchy of continuous and discontinuous transitions depending on lattice connectivity and kinetic constraints. Here the range of the previously observed phase diagram topologies and higher-order singularities is extended to disconnected glass-glass transitions and to cusp and swallowtail bifurcations (which can be generic and degenerate). The phase diagram and the order parameter for two different types of spin mixtures are analytically determined and an experimental realization of the new predictions emerging in our approach is suggested.

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study the fluctuations of dynamical heterogeneity and their finite-size scaling properties in the beta relaxation regime of such microscopic spin models. We compare the critical fluctuations behavior for two distinct measures of correlations with the results of a recently proposed field theoretical description based on quasi-equilibrium ideas. We find that the theoretical predictions perfectly fit the numerical simulation data once the relevant order parameter is identified with the persistence function of the spins.

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the ${\mathsf F}_{12}$ schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamic glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamic facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the ${\mathsf F}_{13}$ schematic model., Comment: Final, published version

Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of highly viscous liquid, the 2D Kob-Andersen kinetically constrained model, driven into non-equilibrium steady states by a uniform non-Hamiltonian force. We present a detailed numerical analysis of the microscopic behavior of the model, including transversal and longitudinal spatial correlations and dynamic heterogeneities. In particular, we show that at high particle density the transition from positive to negative resistance regimes in the current vs field relation can be explained via the emergence of nontrivial structures that intermittently trap the particles and slow down the dynamics. We relate such spatial structures to the current vs field relation in the different transport regimes.

The formal structure of glass singularities in the mode-coupling theory (MCT) of supercooled liquids dynamics is closely related to that appearing in the analysis of heterogeneous bootstrap percolation on Bethe lattices, random graphs and complex networks. Starting from this observation one can build up microscopic on lattice realizations of schematic MCT based on cooperative facilitated spin mixtures. I discuss a microscopic implementation of the F13 schematic model including multiple glassy states and the glass-glass transition. Results suggest that our approach is flexible enough to bridge alternative theoretical descriptions of glassy matter based on the notions of quenched disorder and dynamic facilitation., Comment: 4 pages, 2 figures

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a hybrid glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions., Comment: 4 pages, 3 figures; minor changes

Current fluctuations and related steady state fluctuation relation are investigated in simple coarse-grained lattice-gas analogs of a non-Newtonian fluid driven by a constant and uniform force field, in two regimes of small entropy production. Non-Gaussian current fluctuations and deviations from fluctuation relation are observed and related to the existence of growing amorphous correlations and heterogeneous anomalous diffusion regimes., Comment: 4 pages, 7 figures; minor changes, references added

Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of non-conservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior, negative differential resistance, two-step structural relaxation, dynamical heterogeneity and, possibly, a jamming transition driven by the external field., Comment: 4 pages, 4 figures; revised version: minor changes, added references; to be published

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols., Comment: 4 pages, 4 figures, minor changes, references added. To appear on PRL

A disordered spin model suitable for studying inverse freezing in fragile glass-forming systems is introduced. The model is a microscopic realization of the ``random-first order'' scenario in which the glass transition can be either continuous or discontinuous in thermodynamic sense. The phase diagram exhibits a first-order transition line between two fluid phases terminating at a critical point. When the interacting degrees of freedom are entropically favoured an inverse static glass transition and a double inverse dynamic freezing appear., Comment: 4 pages, 4 figures

We discuss a generic mechanism for shear-thickening analogous to entropy-driven phase reentrance. We implement it in the context of non-relaxational mean-field glassy systems: although very simple, the microscopic models we study present a dynamical phase diagram with second and first order stirring-induced jamming transitions leading to intermittency, metastability and phase coexistence as seen in some experiments. The jammed state is fragile with respect to change in the stirring direction. Our approach provides a direct derivation of a Mode-Coupling theory of shear-thickening., Comment: 4 pages, 4 figures, minor changes, references added

We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These regimes are identified both by a new response function in dynamically available volume, as well as directly in the dynamics. Results for the selfdiffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest., Comment: 11 pages

We show that facilitated spin models of cooperative dynamics introduced by Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar to the one predicted by the mode-coupling theory of supercooled liquids and the dynamical theory of mean-field disordered systems. At low temperature such cooperative models show a two-step relaxation and their equilibration time diverges at a finite temperature according to a power-law. The geometric nature of the dynamical arrest corresponds to a bootstrap percolation process which leads to a phase space organization similar to the one of mean-field disordered systems. The relaxation dynamics after a subcritical quench exhibits aging and converges asymptotically to the threshold states that appear at the bootstrap percolation transition., Comment: 7 pages, 6 figures, minor changes, final version to appear in Europhys. Lett

We investigate the Kovacs (or crossover) effect in facilitated $f$-spin models of glassy dynamics. Although the Kovacs hump shows a behavior qualitatively similar for all cases we have examined (irrespective of the facilitation parameter $f$ and the spatial dimension $d$), we find that the dependence of the Kovacs peak time on the temperature of the second quench allows to distinguish among different microscopic mechanisms responsible for the glassy relaxation (e.g. cooperative vs defect diffusion). We also analyze the inherent structure dynamics underlying the Kovacs protocol, and find that the class of facilitated spin models with $d>1$ and $f>1$ shows features resembling those obtained recently in a realistic model of fragile glass forming liquid., Comment: 7 pages, final version to appear in EPJB, new results and an extended discussion

In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a critical-like dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving Gumbel-like distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma-model approach., Comment: 20 pages, RevTex, 9 figures

We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo simulations of a lattice gas under gravity. The dynamical equation can be thought of as a local density functional theory for a class of lattice gases used to model slow relaxation of glassy and granular materials. The theory predicts a jamming transition line between a low density fluid phase and a high density glassy regime, characterized by diverging relaxation time and logarithmic or power-law compaction according to the specific form of the diffusion coefficient. In particular, we show that the model exhibits history dependent properties, such as quasi reversible-irreversible cycle and memory effects -- as observed in recent experiments, and dynamical heterogeneities., Comment: 14 pages, submitted to Physica A

Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. Rowlands, Comment: To appear In Physical Review Letters

The vortex contribution to the probability density function of longitudinal magnetization fluctuations is examined in finite 2D XY systems close to the Kosterlitz-Thouless-Berezinskii transition temperature. Within the temperature range studied their relevance is limited to rare fluctuations, where they increase the probability of events exceeding four standard deviations below the mean magnetization., Comment: 6 pages, 4 figures. Refs added

The notion of longitudinal effective temperature and its relation with the Edwards compactivity are investigated in an abstract lattice gas model of granular material compacting under gravity and weak thermal vibration., Comment: 4 pages, 4 figures; fig.4 corrected + minor changes. To appear in PRE

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics., Comment: 15 pages, 8 figures. A few references added

Boundary-induced transport in particle systems with anomalous diffusion exhibits rectification, negative resistance, and hysteresis phenomena depending on the way the drive acts on the boundary. The solvable case of a 1D system characterized by a power-law diffusion coefficient and coupled to two particles reservoirs at different chemical potential is examined. In particular, it is shown that a microscopic realisation of such a diffusion model is provided by a 3D driven lattice-gas with kinetic constraints, in which energy barriers are absent and the local microscopic reversibility holds., Comment: 12 pages, 4 figures, minor changes

We study three kinetic models with constraint, namely the Symmetrically Constrained Ising Chain, the Asymmetrically Constrained Ising Chain, and the Backgammon Model. All these models show glassy behavior and coarsening. We apply to them the Stillinger and Weber decomposition, and find that they share the same configurational entropy, despite of their different nonequilibrium dynamics. We conclude therefore that the Stillinger and Weber decomposition is not relevant for this type of models., Comment: 14 pages, 12 figures

We reply to the comment on our published paper `` Universal Fluctuations in Correlated Systems'',Phys. Rev. Lett. Vol; 84, p3744 (2000), by B. Zheng and S. Trimper, cond-mat/0109003. We argue that their results confirm our conjecture, that the probability distribution for order parameter fluctuations in the 2D and 3D Ising models at a temperature $T^{\ast}(L)$ slightly below $T_C$ for the infinite, system approximates the universal functional form of the 2D-XY model in its low temperature phase. We discuss the relevance of the temperature interval $T_C-T^{\ast}$, considered to be large by Zheng and Trimper and explain why the observed phenomena is a critical phenomena., Comment: 1 page, no figures. To appear in Phys. Rev. Lett

One-flip stable configurations of an Ising-model on a random graph with fluctuating connectivity are examined. In order to perform the quenched average of the number of stable configurations we introduce a global order-parameter function with two arguments. The analytical results are compared with numerical simulations., Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev. E

We calculate the probability density function for the order parameter fluctuations in the low temperature phase of the 2D-XY model of magnetism near the line of critical points. A finite correlation length, \xi, is introduced with a small magnetic field, h, and an accurate expression for \xi(h) is developed by treating non-linear contributions to the field energy using a Hartree approximation. We find analytically a series of universal non-Gaussian distributions with a finite size scaling form and present a Gumbel-like function that gives the PDF to an excellent approximation. We propose the Gumbel exponent, a(h), as an indirect measure of the length scale of correlations in a wide range of complex systems., Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev. E

The aging dynamics and the fluctuation-dissipation relation between the spontaneous diffusion induced by a random noise and the drift motion induced by a small stirring force are numerically investigated in a 3D schematic model of compacting powder: a gravity-driven lattice-gas with kinetic constraints. The compaction dynamics is characterized by a super-aging behaviour and, in analogy with glasses, exhibits a purely dynamical time-scale dependent effective temperature. A simple experiment to measure this quantity is suggested., Comment: 4 pages, 4 figures; to appear in Phys. Rev. E

The nonequilibrium critical dynamics of the 2D XY model is investigated numerically through Monte Carlo simulations and analytically in the spin-wave approximation. We focus in particular on the behaviour of the two-time response and correlation functions and show that the ageing dynamics depends on the initial conditions. The presence of critical fluctuations leads to non-trivial violations of the fluctuation-dissipation theorem apparently reminiscent of the three dimensional Edwards-Anderson spin glass model. We compute for this reason the finite-size overlap probability distribution function and find that it is related to the finite-time fluctuation-dissipation ratio obtained in the out of equilibrium dynamics, provided that the temperature is not very low., Comment: Minor changes - Version accepted for publication - Journal of Physics A

We present an analytical approach to the out of equilibrium dynamics of a class of kinetic lattice gases under gravity. The location of the jamming transition, the critical exponents, and the scaling functions characterizing the relaxation processes are determined. In particular, we find that logarithmic compaction and simple aging are intimately related to the Vogel-Fulcher law, while power-law compaction and super-aging behavior occur in presence of a power-law diffusion., Comment: 7 pages, 5 figures. Eq.7 corrected plus minor changes. To appear in Europhys. Lett

We present numerical support for the hypothesis that macroscopic observables of dense granular media can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of finite-dimensional systems and compare its predictions for various observables with the outcome of the out of equilibrium dynamics at large times. We discuss in detail the connection with the effective temperatures that appear in out of equilibrium glass theories, as well as the relation between our computation and those based on `inherent structure' arguments. A short version of this work has appeared in Phys. Rev. Lett. 85, 5034 (2000) (cond-mat/0006140)., Comment: 16 pages, 21 figures

We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent $\eta$. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high resolution molecular dynamics and Monte Carlo simulations. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than four, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behaviour observed in models of interface growth and for dissipative systems driven into a non-equilibrium steady state., Comment: 32 pages, 13 figures, 1 table. Few changes. To appear in Phys. Rev. E

We show that the main dynamical features of granular media can be understood by means of simple models of fragile-glass forming liquid provided that gravity alone is taken into account. In such lattice-gas models of cohesionless and frictionless particles, the compaction and segregation phenomena appear as purely non-equilibrium effects unrelated to the Boltzmann-Gibbs measure which in this case is trivial. They provide a natural framework in which slow relaxation phenomena in granular and glassy systems can be explained in terms of a common microscopic mechanism given by a free-volume kinetic constraint., Comment: 4 pages, 6 figures

Can one construct a thermodynamics for compact, slowly moving powders and grains? A few years ago, Edwards proposed a possible step in this direction, raising the fascinating perspective that such systems have a statistical mechanics of their own, different from that of Maxwell, Boltzmann and Gibbs, allowing us to have some information while still ignoring dynamic details. Recent developments in the theory of glasses have come to confirm these ideas within mean-field. In order to go beyond, we explicitly generate Edwards' measure in a model that, although schematic, is three dimensional. Comparison of the results thus obtained with the irreversible compaction data shows very good agreement. The present framework immediately suggests new experimental checks., Comment: 4 pages, 4 figures; (minor changes, refs. added) to appear in PRL

e discuss the relevance of the Stillinger and Weber approach to the glass transition investigating the non-equilibrium behavior of models with non-trivial dynamics, but with simple equilibrium properties. We consider a family of 1D constrained kinetic models, which interpolates between the asymmetric chain introduced by Eisinger and J\"ackle [Z. Phys. {\bf B84}, 115 (1991)] and the symmetric chain introduced by Fredrickson and Andersen [Phys. Rev. Lett {\bf 53}, 1244 (1984)], and the 1D version of the Backgammon model [Phys. Rev. Lett. {\bf 75}, 1190 (1995)]. We show that the configurational entropy obtained from the inherent structures is the same for all models irrespective of their different microscopic dynamics. We present a detailed study of the coarsening behavior of these models, including the relation between fluctuations and response. Our results suggest that any approach to the glass transition inspired by mean-field ideas and resting on the definition of a configurational entropy must rely on the absence of any growing characteristic coarsening pattern., Comment: 32 pages, 28 figures, RevTeX

Kinetic lattice-gas models display fragile glass behavior, in spite of their trivial Gibbs-Boltzmann measure. This suggests that the nature of glass transition might be, at least in some cases, understood in purely kinetic or dynamical terms., Comment: Invited talk at the Conference: "Unifying Concepts in Glass Physics" ICTP Trieste, September 1999