A test of non-equilibrium thermodynamics in glassy systems: the soft-sphere case

The scaling properties of the soft-sphere potential allow the derivation of an exact expression for the pressure of a frozen liquid, i.e., the pressure corresponding to configurations which are local minima in its multidimensional potential energy landscape. The existence of such a relation offers the unique possibility for testing the recently proposed extension of the liquid free energy to glassy out-of-equilibrium conditions and the associated expression for the temperature of the configurational degrees of freedom. We demonstrate that the non-equilibrium free energy provides an exact description of the soft-sphere pressure in glass states

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.

Intra-molecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intra-molecular interaction $J_\sigma$, using mean field theory and off-lattice Monte Carlo simulations. For all $J_\sigma\geq 0$, the model displays a temperature of maximum density.For a finite intra-molecular interaction $J_\sigma > 0$,our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely pre-empted by inevitable freezing. For J=0 the liquid-liquid critical point disappears at T=0.Comment: 8 pages, 4 figure

Water-like anomalies for core-softened models of fluids: One dimension

We use a one-dimensional (1d) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1d system stems from the facts that closed-form results are possible and that the qualitative behavior in 1d is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point $C'$ at a positive pressure, which is the analog of the T=0 ``critical point'' in the $1d$ Ising model. The existence of point $C'$ leads to anomalous behavior of the isothermal compressibility $K_T$ and the isobaric specific heat $C_P$.Comment: 22 pages, 7 figure