Self-organized criticality in the intermediate phase of rigidity percolation

Abstract

Experimental results for covalent glasses have highlighted the existence of a new self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties of this intermediate phase in more detail. We find that microscopic perturbations, such as the addition or removal of a single bond, can affect the rigidity of macroscopic regions of the network, in particular, creating or destroying percolation. This, together with a power-law distribution of rigid cluster sizes, suggests that the system is maintained in a critical state on the rigid/floppy boundary throughout the intermediate phase, a behavior similar to self-organized criticality, but, remarkably, in a thermodynamically equilibrated state. The distinction between percolating and non-percolating networks appears physically meaningless, even though the percolating cluster, when it exists, takes up a finite fraction of the network. We point out both similarities and differences between the intermediate phase and the critical point of ordinary percolation models without self-organization. Our results are consistent with an interpretation of recent experiments on the pressure dependence of Raman frequencies in chalcogenide glasses in terms of network homogeneity.

arXiv comment20 pages, 18 figures

References in corpus (8)

• Rings and rigidity transitions in network glasses
• Pressure Raman effects and internal stress in network glasses
• On adaptability and "intermediate phase" in randomly connected networks
• Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices
• Self-organization with equilibration: a model for the intermediate phase in rigidity percolation
• First-order rigidity transition on Bethe Lattices
• Rigidity transitions and constraint counting in amorphous networks: beyond the mean-field approach
• The Thermally Reversing Window in Ternary GexPxS1-2x glasses

Cited by in corpus (14)

• Relaxation and physical aging in network glasses: a review
• Intermediate phase, network demixing, boson and floppy modes, and compositional trends in glass transition temperatures of binary AsxS1-x system
• Melt homogenization and self-organization of chalcogenides glasses: evidence of sharp rigidity, stress and nanoscale phase separation transitions in the GexSe100-x binary
• Rigid cluster decomposition reveals criticality in frictional jamming
• Abrupt boundaries of intermediate phases and space filling in oxide glasses
• Intermediate Phases, structural variance and network demixing in chalcogenides: the unusual case of group V sulfides
• Meeting experimental challenges to physics of network glasses: assessing role of sample homogeneity
• Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios
• Force networks and jamming in shear deformed sphere packings
• On the Dynamics of Glassy Systems
• Hierarchical models of rigidity percolation
• Plasticity-rigidity cycles: A general adaptation mechanism
• Adaptive Elastic Networks as models of supercooled liquids
• Control of connectivity and rigidity in prismatic assemblies