Phase diagram of a hard-sphere system in a quenched random potential:  A numerical study

Abstract

We report numerical results for the phase diagram in the density-disorder plane of a hard sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed. 64.70.Pf, 64.60.Ak, 64.60.Cn

Vortices in layered superconductors with columnar pins: A density-functional study

“…This precludes the use of many standard minimization methods. The procedure we use here is the same as that originally employed in the hard sphere problem 29,34,35 with the important difference that the calculations involving the interacting term are performed in wavevector space. This is for two reasons: first, it turns out to be much more efficient, since the time used by Fourier transforming back and forth using efficient FFT routines turns out to be negligible compared with the time saved by not having to perform a double sum over the large computational lattice.…”

Equilibrium Glassy Phase in a Polydisperse Hard-Sphere System

“…For such systems, glass (amorphous solid) is believed to be a metastable phase [2], resulting from structural arrest. However, in recent theoretical studies [3,4] of hard spheres in the presence of a quenched random potential, an equilibrium glassy phase was observed at high disorder strengths. While this phenomenon has not yet been confirmed experimentally, it brings forth the question of whether even the presence of annealed disorder in a system of hard spheres can result in an equilibrium glassy phase.…”

Vortex Lattice Melting in Layered Superconductors with Periodic Columnar Pins

“…Using density functional theory [10,11] and a newly developed numerical method [12] that is uniquely suited for calculations of pinning-induced inhomogeneities in the local density, we have studied the effects of this periodic potential on the structure and thermodynamics of the liquid and crystalline states of a system of "pancake" vortices [8] in a highly anisotropic layered superconductor. For small concentrations of pinning centers, we find a first-order melting transition from a crystalline solid to a modulated liquid.…”

“…(2), we discretize space by defining density variables ͕r k ͖ at the sites of a periodic grid, and use a gradient descent method [12] to locate the minima of the free energy of Eq. (2) written as a function of ͕r k ͖.…”