Elasticity and metastability limit in supercooled liquids: a lattice model

We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models. The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.Comment: 8 pages, 5 figure

Replica symmetry breaking in long-range glass models without quenched disorder

We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The formalism is applied to the long range Ising model with orthogonal coupling matrix. We find the one step replica-symmetry breaking solution and show that it is stable in the intermediate temperature range that includes the glass state but excludes very low temperatures. At very low temperatures this solution becomes unstable and this approach fails.Comment: 6 pages, 2 figure

Frequency-domain study of relaxation in a spin glass model for the structural glass transition

We have computed the time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM). We find that for temperatures above the mode-coupling temperature the imaginary part of the susceptibility $\chi''(\nu)$ obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of $\chi''$ decreases following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ where the configurational entropy vanishes.Comment: 7 pages, 4 figures, epl LaTeX packag

Glassy Mean-Field Dynamics of the Backgammon model

In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of {\it entropy barriers} in configuration space. The model is simple enough to allow for a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow to study the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure

Configurational Entropy and its Crisis in Metastable States: Ideal Glass Transition in a Dimer Model as a Paragidm of a Molecular Glass

We discuss the need for discretization to evaluate the configurational entropy in a general model. We also discuss the prescription using restricted partition function formalism to study the stationary limit of metastable states. We introduce a lattice model of dimers as a paradigm of molecular fluid and study metastability in it to investigate the root cause of glassy behavior. We demonstrate the existence of the entropy crisis in metastable states, from which it follows that the entropy crisis is the root cause underlying the ideal glass transition in systems with particles of all sizes. The orientational interactions in the model control the nature of the liquid-liquid transition observed in recent years in molecular glasses.Comment: 36 pages, 9 figure

Free Energy Landscape Of Simple Liquids Near The Glass Transition

Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local minima of the free energy are located and the distribution of an appropriately defined ``overlap'' between minima is calculated. The process of transition from the basin of attraction of a minimum to that of another one is studied using a new ``microcanonical'' Monte Carlo procedure, leading to a determination of the effective height of free energy barriers that separate different glassy minima. The general appearance of the free energy landscape resembles that of a putting green: deep minima separated by a fairly flat structure. The growth of the effective free-energy barriers with increasing density is consistent with the Vogel-Fulcher law, and this growth is primarily driven by an entropic mechanism.Comment: 10 pages, 6 postscript figures, uses iopart.cls and iopart10.clo (included). Invited talk at the ICTP Trieste Conference on "Unifying Concepts in Glass Physics", September 1999. To be published in J. Phys. Cond. Ma

A teaching guide of nuclear physics: the concept of bonds

We propose discussions and hands-on activities for GCSE and A-level students, covering a fundamental aspect of nuclear physics: the concept of bond and the energy released (absorbed) when a bond is created (broken). This is the first of the series of papers named "A teaching guide of nuclear physics", whose main goal is to provide teaching tools and ideas to GCSE and A-level teachers, within a consistent and complete curriculum

Solvent-induced micelle formation in a hydrophobic interaction model

We investigate the aggregation of amphiphilic molecules by adapting the two-state Muller-Lee-Graziano model for water, in which a solvent-induced hydrophobic interaction is included implicitly. We study the formation of various types of micelle as a function of the distribution of hydrophobic regions at the molecular surface. Successive substitution of non-polar surfaces by polar ones demonstrates the influence of hydrophobicity on the upper and lower critical solution temperatures. Aggregates of lipid molecules, described by a refinement of the model in which a hydrophobic tail of variable length interacts with different numbers of water molecules, are stabilized as the length of the tail increases. We demonstrate that the essential features of micelle formation are primarily solvent-induced, and are explained within a model which focuses only on the alteration of water structure in the vicinity of the hydrophobic surface regions of amphiphiles in solution.Comment: 11 pages, 10 figures; some rearrangement of introduction and discussion sections, streamlining of formalism and general compression; to appear in Phys. Rev.

Mean field theory of hard sphere glasses and jamming

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings.Comment: 59 pages, 25 figures. Final version published on Rev.Mod.Phy

Free energy and configurational entropy of liquid silica: fragile-to-strong crossover and polyamorphism

Recent molecular dynamics (MD) simulations of liquid silica, using the ``BKS'' model [Van Beest, Kramer and van Santen, Phys. Rev. Lett. {\bf 64}, 1955 (1990)], have demonstrated that the liquid undergoes a dynamical crossover from super-Arrhenius, or ``fragile'' behavior, to Arrhenius, or ``strong'' behavior, as temperature $T$ is decreased. From extensive MD simulations, we show that this fragile-to-strong crossover (FSC) can be connected to changes in the properties of the potential energy landscape, or surface (PES), of the liquid. To achieve this, we use thermodynamic integration to evaluate the absolute free energy of the liquid over a wide range of density and $T$. We use this free energy data, along with the concept of ``inherent structures'' of the PES, to evaluate the absolute configurational entropy $S_c$ of the liquid. We find that the temperature dependence of the diffusion coefficient and of $S_c$ are consistent with the prediction of Adam and Gibbs, including in the region where we observe the FSC to occur. We find that the FSC is related to a change in the properties of the PES explored by the liquid, specifically an inflection in the $T$ dependence of the average inherent structure energy. In addition, we find that the high $T$ behavior of $S_c$ suggests that the liquid entropy might approach zero at finite $T$, behavior associated with the so-called Kauzmann paradox. However, we find that the change in the PES that underlies the FSC is associated with a change in the $T$ dependence of $S_c$ that elucidates how the Kauzmann paradox is avoided in this system. Finally, we also explore the relation of the observed PES changes to the recently discussed possibility that BKS silica exhibits a liquid-liquid phase transition, a behavior that has been proposed to underlie the observed polyamorphism of amorphous solid silica.Comment: 14 pages, 18 figure