Condensation of helium in aerogel and athermal dynamics of the random-field Ising model

Inverse transitions and disappearance of the λ-line in the asymmetric random-field Ising and Blume-Capel models

We report on reentrance in the random-field Ising and Blume-Capel models, induced by an asymmetric bimodal random-field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the λ-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first-order transition lines that always end at ordered critical points. We find that, while for symmetric random-field distributions there is no reentrance, the asymmetry in the random-field results in a range of temperatures for which magnetization shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first-order inverse phase transitions that ends at an inverse-ordered critical point. We show that the location of the inverse transitions can be inferred from the ground-state phase diagram of the model.

Finite Dimensional Vestige of Spinodal Criticality above the Dynamical Glass Transition

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.

On Condensation and Evaporation Mechanisms in Disordered Porous Materials

Sorption isotherm measurement is a standard method for characterizing porous materials. However, such isotherms are generally hysteretic, differing between condensation and evaporation. Quantitative measurement of pore diameter distributions requires proper identification of the mechanisms at play, a topic which has been and remains the subject of intensive studies. In this paper, we compare high-precision measurements of condensation and evaporation of helium in Vycor, a prototypical disordered porous glass, to a model incorporating mechanisms on the single pore level through a semimacroscopic description and collective effects through lattice simulations. Our experiment determines both the average of the fluid density through volumetric measurements and its spatial fluctuations through light scattering. We show that the model consistently accounts for the temperature dependence of the isotherm shape and of the optical signal over a wide temperature range as well as for the existence of thermally activated relaxation effects. This demonstrates that the evaporation mechanism evolves from pure invasion percolation from the sample's surfaces at the lowest temperature to percolation from bulk cavitated sites at larger temperatures. The model also shows that the experimental lack of optical signals during condensation does not imply that condensation is unaffected by network effects. In fact, these effects are strong enough to make most pores to fill at their equilibrium pressure, a situation deeply contrasting the behavior for isolated pores. This implies that, for disordered porous materials, the classical Barrett-Joyner-Halenda approach, when applied to the condensation branch using an extended version of the Kelvin equation, should properly measure the true pore diameter distribution. Our experimental results support this conclusion.

A single-walker approach for studying quasi-nonergodic systems

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-nonergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.

Imbibition Triggered by Capillary Condensation in Nanopores

We study the spatiotemporal dynamics of water uptake by capillary condensation from unsaturated vapor in mesoporous silicon layers (pore radius r_p ≃ 2 nm), taking advantage of the local changes in optical reflectance as a function of water saturation. Our experiments elucidate two qualitatively different regimes as a function of the imposed external vapor pressure: at low vapor pressures, equilibration occurs via a diffusion-like process; at high vapor pressures, an imbibition-like wetting front results in fast equilibration toward a fully saturated sample. We show that the imbibition dynamics can be described by a modified Lucas-Washburn equation that takes into account the liquid stresses implied by Kelvin equation.

Spinodals with Disorder: From Avalanches in Random Magnets to Glassy Dynamics

We revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. We focus on the spinodal of an Ising model in a quenched random field (RFIM), which has applications in many areas from materials to social science. By working at zero temperature in the quasistatically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the latter is due to the depinning and the subsequent expansion of rare droplets. We work out the associated critical behavior, which, in any finite dimension, is very different from the mean-field one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild nonanalyticities much like in a Griffith phenomenon. From the recently established connection between the spinodal of the RFIM and glassy dynamics, our results also allow us to conclusively assess the physical content and the status of the dynamical transition predicted by the mean-field theory of glass-forming liquids.

Statistical mechanics of unsaturated porous media

We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network.