Reversible first-order transition in Pauli percolation

Abstract

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyse a new percolation problem in which the first order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight $W(n)=n+1$ for a cluster of size $n$. This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle, and their reach in practice.

4 pages + Supplementary Materials

References in corpus (6)

• Avoiding a Spanning Cluster in Percolation Models
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Cavity method for quantum spin glasses on the Bethe lattice
• Using explosive percolation in analysis of real-world networks
• There are no Goldstone bosons on the Bethe lattice
• Ensemble inequivalence in random graphs

Cited by in corpus (6)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Scattering matrix invariants of Floquet topological insulators
• Crossover phenomena of percolation transition in evolution networks with hybrid attachment
• Hubbard models with nearly flat bands: Ground-state ferromagnetism driven by kinetic energy
• Theory of deflagration in disordered media
• Quantum Heisenberg antiferromagnet in a field on the Tasaki square lattice