J. M. Schwarz et al 2006 Europhys. Lett. 73 560 doi:10.1209/epl/i2005-10421-7
J. M. Schwarz1,2, A. J. Liu1,2 and L. Q. Chayes3
Show affiliationsA theory is constructed to describe the zero-temperature jamming transition of repulsive soft spheres as the density 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 reminiscent of the jamming transition. In particular, the exponents characterizing the continuous parts of both transitions appear to be the same. Finally, numerical simulations suggest that in finite dimensions the k-core transition can be discontinuous with a nontrivial diverging correlation length.
64.70.P- Glass transitions of specific systems
64.60.A- Specific approaches applied to studies of phase transitions
Issue 4 (February 2006)
Received 22 June 2005, accepted for publication 12 December 2005, in final form 12 December 2005
Published 13 January 2006
J. M. Schwarz et al 2006 Europhys. Lett. 73 560
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