On $k$-Core Percolation in Four Dimensions

Details On $k$-Core Percolation in Four Dimensions On $k$-Core Percolation in Four Dimensions

2006-09-29

arxiv.org/abs/cond-mat/0609777v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

The $k$-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order/second-order nature. We investigate numerically $k$-core percolation on the four-dimensional regular lattice. For $k=4$ the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the $k$-core density displays no singular behavior before the jump and its correlation length remains finite. For $k=3$ the transition is continuous.

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