Real-space renormalization of randomly vacated lattices: a renormalization group for jamming?

摘要

Jamming occurs in granular materials, emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction phi, defined as the ratio of particle volume to system volume, is increased past a critical value phi c a liquid-solid phase transition occurs, and grains are no longer able to rearrange. Previous studies have shown evidence of spatial correlations that diverge near phi=phi c, but there has been no explicit spatial renormalization group (RG) scheme that has captured this transition. Here, I present a candidate for such a scheme, using a block-spin-like transformation of a randomly vacated lattice of grains. I define a real-space RG transformation based on local mechanical stability. This model displays a critical packing fraction phi cdocumentclas and gives estimates of critical exponents in two and three dimensions.