On $k$-Core Percolation in Four Dimensions

Abstract

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.

References in corpus (3)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
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Cited by in corpus (14)

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• Percolation on complex networks: Theory and application
• Core percolation on complex networks
• Articulation Points in Complex Networks
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Inducing Effect on the Percolation Transition in Complex Networks
• Controlling the uncertain response of real multiplex networks to random damage
• Mutually cooperative epidemics on power-law networks
• On the study of force-balance percolation
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Fractal fluctuations at mixed-order transitions in interdependent networks
• Dynamics of k-core percolation in a random graph
• Effect of network clustering on mutually cooperative coinfections
• Selective Bootstrap Percolation