The fate of the bootstrap percolation hybrid critical point in finite dimension

TL;DR

This paper investigates the fate of the hybrid phase transition in bootstrap percolation within finite dimensions, revealing it does not persist but still models critical behavior akin to supercooled liquids.

Contribution

It applies the M-layer technique to analyze corrections to mean-field theory, showing the hybrid transition is an avoided transition in finite dimensions.

Findings

Hybrid transition does not survive in physical dimensions.

The problem maps to a spinodal with quenched disorder.

Critical properties serve as a proxy for Mode-Coupling-Theory critical point.

Abstract

Bootstrap, or $k$-core, percolation displays on the Bethe lattice a mixed first/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.