Jamming as a critical phenomenon: a field theory of zero-temperature grain packings

TL;DR

This paper develops a field theory describing a zero-temperature critical point in two-dimensional frictionless grain packings, revealing a phase transition characterized by force and contact number order parameters with diverging fluctuations.

Contribution

It introduces a novel field-theoretic framework for understanding the jamming transition as a critical phenomenon at zero temperature in 2D frictionless packings.

Findings

Critical point exhibits a mixed transition with discontinuous order parameters and diverging force fluctuations.

Distribution of contact forces shows a plateau at the critical point, matching experimental observations.

Theory predicts spatial force fluctuation behaviors and discusses extensions to finite temperature and frictional systems.

Abstract

A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a non-zero value of the packing fraction. The zero-temperature constraint of force-balance plays a crucial role in determining the nature of the transition. Two order parameters, <z>, the deviation of the average number of contacts from the isostatic value and, <F>, the average magnitude of the force per contact, characterize the transition from the jammed (high packing fraction) to the unjammed (low packing fraction state). The critical point has a mixed character with the order parameters showing a jump discontinuity but with fluctuations of the contact force diverging. At the critical point, the distribution of F shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces. Implications for finite temperature dynamics and generalizations to frictional packings and higher dimensions are discussed