The onset of jamming as the sudden emergence of an infinite $k$-core cluster

J. M. Schwarz; A. J. Liu; L. Q. Chayes

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The onset of jamming as the sudden emergence of an infinite $k$-core cluster

J. M. Schwarz·A. J. Liu·L. Q. Chayes

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Abstract

A theory is constructed to describe the zero-temperature jamming transition as the density of repulsive soft spheres is increased. Local mechanical stability imposes a constraint on the minimum number of bonds per particle; we argue that this constraint suggests an analogy to $k$-core percolation. The latter model can be solved exactly on the Bethe lattice, and the resulting transition has a mixed first-order/continuous character. The exponents characterizing the continuous part appear to be the same as for the jamming transition. Finally, numerical simulations suggest that in finite dimensions the $k$-core transition can be discontinuous with a nontrivial diverging correlation length.

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J. M. Schwarz, A. J. Liu, L. Q. Chayes. 2005-11-02. The onset of jamming as the sudden emergence of an infinite $k$-core cluster. https://arxiv.org/abs/cond-mat/0410595

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