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

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.

Discussion of the $M$-layer construction in the Renormalization Group framework added. Accepted for publication on Phys. Rev. Lett

References in corpus (12)

• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Critical phenomena in heterogeneous k-core percolation
• Critical behavior of $k$-core percolation: Numerical studies
• Spiral Model: a cellular automaton with a discontinuous glass transition
• Long-wavelength fluctuations lead to a model of the glass crossover
• Loop expansion around the Bethe approximation through the $M$-layer construction
• The jamming transition is a k-core percolation transition
• Scaling and universality in glass transition
• On the study of jamming percolation
• Dynamics of k-core percolation in a random graph
• The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions
• The large connectivity limit of bootstrap percolation

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• Suppression of spinodal instability by disorder in an athermal system
• Hierarchical cycle-tree packing model for $K$-core attack problem
• Bethe $M$-layer construction for the percolation problem
• Vulnerability and Resilience of Social Engagement: Equilibrium Theory
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Bethe $M$-layer construction on the Ising model
• Critical exponents of the spin glass transition in a field at zero temperature
• Theory of Kinetically-Constrained-Models Dynamics
• K-core attack, equilibrium K-core, and kinetically constrained spin system
• Selective Bootstrap Percolation
• Asymptotically Exact Solution of the Fredrickson-Andersen Model
• Long-range spin glass in a field at zero temperature