Weakly first-order transition in an athermal lattice gas.

We investigate the phase behavior of a two-dimensional athermal lattice gas in which every hard-core particle can have two or fewer nearest neighboring occupied sites on the square lattice. The ground state and close packing density are determined and it is found that at large chemical potential the model undergoes an ordering phase transition with preferential sublattice occupation. Although near the transition point the particle density and entropy exhibit an apparent discontinuity, we find that the order parameter and fluctuations of thermodynamic quantities do not scale with the system volume. These paradoxical results are reconciled by analyzing the size-dependent flow of the thermal exponent by phenomenological renormalization and the curve-crossing method, which lead to a weakly first-order phase transition scenario.

First-order phase transition in a two dimensional BM3 model.

The phase behavior of a Biroli-Mézard model on the two dimensional square lattice in which hard-core particles can have at most three nearest neighboring occupied sites is investigated by means of grand-canonical Monte Carlo simulations. Finite-size scaling analysis of relevant thermodynamic quantities obtained via the histogram reweighting technique reveals that at high-density, the model undergoes a first-order phase transition with preferential sublattice occupation to a crystal phase with enantiomorph ground state configurations, in close analogy to the hard-core lattice gas with the exclusion range extended up to the third shell of nearest neighbors.

Fluctuation-induced forces in driven systems with a diffusivity anomaly.

We show that Casimir-like forces in boundary-driven systems with a bulk diffusivity anomaly are enhanced by cooperative dynamical effects and can be made locally attractive or repulsive depending on the boundary densities. Theoretical predictions based on mean-field arguments and the explicit evaluation of the Casimir force in the fluctuating hydrodynamics framework are supported by Monte Carlo simulation of a two-dimensional (2D) exclusion process with selective kinetic constraints. Consistent with the entropic interpretation of the Casimir effect, we find that local repulsive forces do appear whenever finite-size transverse density fluctuations exceed their infinite-size value. Our results suggest that the bulk diffusivity anomaly is a crucial ingredient in the small-scale design of driven soft-matter systems with tunable fluctuation-induced forces.

Measuring pressure in equilibrium and nonequilibrium lattice-gas models.

We develop an algorithm based on the method proposed by Dickman for directly measuring pressure in lattice-gas models. The algorithm gives the possibility to access the equation of state with a single run by adding multiple ghost sites to the original system. This feature considerably improves calculations and makes the algorithm particularly efficient for systems with inhomogeneous density profiles, both in equilibrium and nonequilibrium steady states. We illustrate its broad applicability by considering some paradigmatic systems of statistical mechanics such as the lattice gas under gravity, nearest-neighbor exclusion models in finite dimension and on regular random graphs, and the boundary-driven simple symmetric exclusion process.

Cooperative transport with selective kinetic constraints.

We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can be concave, convex, or both, depending on the density of boundary particle reservoirs. A mean-field analysis based on a diffusion equation with a density-dependent diffusion coefficient qualitatively reproduces this behavior, and suggests its occurrence in liquids with a diffusivity anomaly.

Nonequilibrium phase transition in constrained adsorption.

We study the adsorption-desorption of fluid molecules on a solid substrate by introducing a schematic model in which the adsorption/desorption transition probabilities are given by irreversible kinetic constraints with a tunable violation of local detailed balance condition. Numerical simulations show that in one spatial dimension, the model undergoes a continuous nonequilibrium phase transition whose location depends on the irreversibility strength. We show that the hierarchy of equations obeyed by multipoint correlation functions can be closed to the second order by means of a simple decoupling approximation and that the approximated solution for the steady state yields a very good description of the overall phase diagram.

Crossover from ß to α Relaxation in Cooperative Facilitation Dynamics.

ß and α relaxation processes are dynamical scaling regimes of glassy systems occurring on two separate time scales which both diverge as the glass state is approached. We study here the crossover scaling from ß to α relaxation in the cooperative facilitation scenario (CFS) and show that it is quantitatively described, with no adjustable parameter, by the leading order asymptotic formulas for scaling predicted by the mode-coupling theory (MCT). These results establish (i) the mutual universality of the MCT and CFS, and (ii) the existence of a purely dynamic realization of MCT, which is distinct from the well-established random first order transition scenario for disordered systems. Some implications of the emerging kinetic-static duality are discussed.

Percolation approach to glassy dynamics with continuously broken ergodicity.

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 the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the F(12) 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 predictions for dynamic relaxation exponents below an upper critical dimension of 6.

Disconnected glass-glass transitions and swallowtail bifurcations in microscopic spin models with facilitated dynamics.

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.

Cooperative heterogeneous facilitation: multiple glassy states and glass-glass transition.

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 F(13) 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.

Driving kinetically constrained models into nonequilibrium steady states: Structural and slow transport properties.

Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at a theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of a highly viscous liquid, the two-dimensional Kob-Andersen kinetically constrained model, driven into nonequilibrium 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.

Microscopic models of mode-coupling theory: the F12 scenario.

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the 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 dynamical 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 dynamical 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 F(13) schematic model.

Dynamic facilitation picture of a higher-order glass singularity.

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 discontinuous 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.

Fluctuation relation and heterogeneous superdiffusion in glassy transport.

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.

Statistical mechanics of combinatorial auctions.

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.

Shear-thickening and entropy-driven reentrance.

We discuss a generic mechanism for shear thickening analogous to entropy-driven phase reentrance. We implement it in the context of nonrelaxational 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.

Geometry of dynamically available empty space is the key to near-arrest dynamics.

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 self-diffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest.

Effective temperature and compactivity of a lattice gas under gravity.

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.

Driven lattice gas as a ratchet and pawl machine.

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 one-dimensional (1D) system characterized by a power-law diffusion coefficient and coupled to two particle reservoirs at different chemical potential is examined. In particular, it is shown that a microscopic realization 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.