Glass transition in the hard sphere system

Dasgupta, Chandan; Valls, Oriol T.

doi:10.1007/bfb0104820

Cited by 5 publications

(16 citation statements)

References 14 publications

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“…that all the transition and instability lines in our phase diagrams lie at substantially lower densities than those obtained in the analytic study, have the same origin as the discrepancy between our s = 0 results and those of molecular dynamics simulations [32] of the pure hard sphere system. As noted in our earlier work [25,28], these differences result from the discretization of the free energy functional. The use of a simple cubic mesh of spacing h ∼ 0.2σ in the discretization procedure increases the relative stability of inhomogeneous local minima of the free energy and thus leads to substantially lower values for the densities at which crystallization and the glass transition occur.…”

Section: Summary and Discussionmentioning

confidence: 83%

“…Consider first the previously studied [24,27,28] case of the disorder-free system (s = 0 line). There, only the uniform liquid minimum is present at low densities.…”

Section: A General Considerations: Phase Diagrammentioning

confidence: 99%

“…If they are incommensurate, only the glassy minima are present. We have carried out extensive numerical investigations of the resulting free-energy landscape [25][26][27][28] in the absence of disorder. In the present study, and with the physical situations described above in mind, we develop similar numerical methods to find the location and structure of the local minima of the same model free energy with the addition of the presence of a time-independent, random, one-body potential.…”

Section: Introductionmentioning

confidence: 99%

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

Dasgupta

Valls

2000

Phys. Rev. E

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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

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Section: Summary and Discussionmentioning

confidence: 83%

“…Consider first the previously studied [24,27,28] case of the disorder-free system (s = 0 line). There, only the uniform liquid minimum is present at low densities.…”

Section: A General Considerations: Phase Diagrammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Dasgupta

Valls

2000

Phys. Rev. E

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“…the structure factor S(k) = |ρ(k)| 2 /N v . We can further characterize the structure of a minimum by analyzing additional information [13] contained in the full set {ρ j }. In particular, we have calculated the local peak densities, defined as the values of the density at local peaks.…”

mentioning

confidence: 99%

“…The local peak density is substantially lower near the grain boundaries. As these minima are warmed up [13], the regions near the grain boundaries begin to "melt" before the other parts of the sample. As shown in panel (c) of Fig.1, the structure factor for these minima exhibits several (typically more than six) peaks of height much lower than that of the six Bragg peaks found for the BrG minimum.…”

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confidence: 99%

Two-Step Melting of the Vortex Solid in Layered Superconductors with Random Columnar Pins

Dasgupta

Valls

2003

Phys. Rev. Lett.

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We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.PACS numbers: 74.25. Qt,74.72.Hs,,74.25.Ha,74.78.Bz The mixed phase of type-II superconductors with random pinning constitutes an excellent test system for studies of the effects of quenched disorder on the structure and melting of crystalline solids. In systems with weak random point pinning, the existence of a lowtemperature topologically ordered Bragg glass (BrG) phase with quasi-long-range translational order is now well established [1,2]. A variety of fascinating "glassy" behavior has been experimentally observed [3] near the first-order melting transition of the BrG phase in both conventional and high-T c superconductors. It has been suggested [3,4] that these observations can be understood if it is assumed that the melting of the BrG phase occurs in two steps: the BrG first transforms into a "multidomain" glassy phase which melts into the usual vortex liquid at a slightly higher temperature.In the presence of random columnar pinning, a "strong" Bose glass (BoG) phase [5] without quasi-longrange translational order occurs at low temperatures if the concentration of pins is larger than that of vortex lines. In the opposite limit of dilute pins, one expects [6] a "weak" BoG phase at low temperatures which would melt into an interstitial liquid (IL) as the temperature is increased. In the IL phase, some of the vortices remain pinned at the strong pinning centers, while the other, interstitial ones form a liquid. A recent numerical study [7] suggests that a topologically ordered BrG phase is also possible in such systems if the pin concentration is sufficiently small. It is also found experimentally, for both point [8] and columnar [9] pinning, that the melting of the solid phase is "broadened": the local transition temperature, measured by a discontinuity of the local magnetization, is different in different regions of the sample.Here we report results of a numerical study that provides insights and explanations for some of the observations described above. From minimization of an appropriate free energy functional, we find that the vortex system in an extremely anisotropic, layered, superconductor with a random dilute array of strong columnar pins (with both pins and magnetic field perpendicular to the layers) forms a BrG phase at low temperatures. As T is increased, this phase undergoes a first order transition into a glassy phase which we identify as a polycrystalline BoG. This phase then transforms, at a slightly higher T , into th...

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Dynamical phase transitions in glasses induced by the ruggedness of the free-energy landscape

Ritort¹

2000

J. Phys.: Condens. Matter

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We propose damage spreading (DS) as a tool to investigate the topological features related to the ruggedness of the free energy landscape. We argue that DS measures the positiveness of the largest Lyapunov exponent associated to the basins of attraction visited by the system during its dynamical evolution. We discuss recent results obtained in the framework of mode-coupling theory and comment how to extend them to the study of realistic glasses. Preliminary results are presented for purely repulsive soft-sphere glasses.

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Glass transition in the hard sphere system

Cited by 5 publications

References 14 publications

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

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

Two-Step Melting of the Vortex Solid in Layered Superconductors with Random Columnar Pins

Dynamical phase transitions in glasses induced by the ruggedness of the free-energy landscape

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