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Packing hard spheres with short-range attraction in infinite dimension: Phase structure and algorithmic implications | | Mauro Sellitto
; Francesco Zamponi
; | | Date: |
12 Sep 2013 | | Abstract: | We study, via the replica method of disordered systems, the packing problem
of hard-spheres with a square-well attractive potential when the space
dimensionality, d, becomes infinitely large. The phase diagram of the system
exhibits reentrancy of the liquid-glass transition line, two distinct glass
states and a glass-to-glass transition, much similar to what has been
previously obtained by Mode-Coupling Theory, numerical simulations and
experiments. The presence of the phase reentrance implies that for a suitable
choice of the intensity and attraction range, high-density sphere packings more
compact than the one corresponding to pure hard-spheres can be constructed in
polynomial time in the number of particles (at fixed, large d) for packing
fractions smaller than 6.5 d 2^{-d}. Although our derivation is not a formal
mathematical proof, we believe it meets the standards of rigor of theoretical
physics, and at this level of rigor it provides a small improvement of the
lower bound on the sphere packing problem. | | Source: | arXiv, 1309.3218 | | Services: | Forum | Review | PDF | Favorites | |
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