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Re-entrant Melting in Polydisperse Hard Spheres

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Paul Bartlett, Patrick B. Warren

Soft Condensed Matter · Submitted 2 Feb 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram.

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arXiv IDcond-mat/9902029 (version 1)
Pith IDSP5RL44G, Pith's permanent record of this paper and its review
CitationPatrick B. Warren, Paul Bartlett. "Re-entrant Melting in Polydisperse Hard Spheres." arXiv:cond-mat/9902029 (1999). https://pith.science/paper/SP5RL44G
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,836 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.29 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. The two transitions converge to a single point which we identify as the polydisperse analogue of a point of equal concentration. At this point, the freezing transition is continuous in a thermodynamic sense.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. contribution 0.78 0.80 0.04 asserted 0.88
s1 At low polydispersities a single fluid-to-crystal transition is recovered. result 0.99 0.59 0.07 asserted 1.00
s2 With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. result 1.00 0.94 0.51 asserted 1.00
s3 The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. result 1.00 0.88 0.36 asserted 1.00
s4 The two transitions converge to a single point which we identify as the polydisperse analogue of a point of equal concentration. interpretation 0.73 0.89 0.22 asserted 1.00
s5 At this point, the freezing transition is continuous in a thermodynamic sense. result 0.57 0.84 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.94 · evidence from proof or derivation 0.69.

What was examined, and what was not

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. The two transitions converge to a single point which we identify as the polydisperse analogue of a point of equal concentration. At this point, the freezing transition is continuous in a thermodynamic sense.

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