On $k$-Core Percolation in Four Dimensions
Disordered Systems and Neural Networks
2012-10-31 v1
Abstract
The -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 -core percolation on the four-dimensional regular lattice. For the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the -core density displays no singular behavior before the jump and its correlation length remains finite. For the transition is continuous.
Keywords
Cite
@article{arxiv.cond-mat/0609777,
title = {On $k$-Core Percolation in Four Dimensions},
author = {Giorgio Parisi and Tommaso Rizzo},
journal= {arXiv preprint arXiv:cond-mat/0609777},
year = {2012}
}