Fate of the Hybrid Transition of Bootstrap Percolation in Physical Dimension

Bootstrap, or k-core, percolation displays on the Bethe lattice a mixed first- and second-order phase transition with both a discontinuous order parameter and diverging critical fluctuations. I apply the recently introduced M-layer technique to study corrections to mean-field theory showing that at all orders in the loop expansion the problem is equivalent to a spinodal with quenched disorder. This implies that the mean-field hybrid transition does not survive in physical dimension. Nevertheless, its critical properties as an avoided transition make it a proxy of the avoided mode-coupling-theory critical point of supercooled liquids.