Journal of Statistical Physics

, Volume 167, Issue 3–4, pp 735–748 | Cite as

Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition

  • Marco Baity-Jesi
  • Carl P. Goodrich
  • Andrea J. Liu
  • Sidney R. Nagel
  • James P. Sethna


We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.


Granular materials Shear jamming Disordered solids Finite-size scaling Scaling theory Jamming Linear elasticity 



The authors owe a great intellectual debt to Leo Kadanoff. His demonstration of how scaling arguments can be used to understand and categorize the universality of physical phenomena was an inspiration for many of the ideas in this paper. His catholic taste in choosing problems, his success in developing simple models to understand complex phenomena, and his complete lack of snobbishness in deciding what problems were important allowed theory and experiment to work together to make progress throughout many areas of science. We dedicate this paper in his memory. We thank Valerio Astuti, Eric DeGiuli, Edan Lerner and Pierfrancesco Urbani for interesting discussions. This work was funded by the Simons Foundation for the collaboration “Cracking the Glass Problem” (454945 to A.J.L. for A.J.L. and J.P.S., 348126 to S.R.N. for S.R.N., and 454935 to G. Biroli for M.B.-J.), the National Science Foundation (DMR-1312160 for J.P.S.), the ERC Grant NPRGGLASS (279950 for M.B.-J.), and the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-05ER46199 (C.P.G.). M.B.-J. was also supported by MINECO, Spain, through the research Contract No. FIS2012-35719-C02, and by the FPU Program (Beca FPU, AP-2010-1318) (Ministerio de Educación, Spain).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Marco Baity-Jesi
    • 1
    • 2
  • Carl P. Goodrich
    • 2
    • 3
  • Andrea J. Liu
    • 2
  • Sidney R. Nagel
    • 4
  • James P. Sethna
    • 5
  1. 1.Institut de Physique Théorique, DRF, CEASaclayFrance
  2. 2.Department of Physics and AstronomyUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA
  4. 4.James Franck Institute, Enrico Fermi Institute, Department of PhysicsThe University of ChicagoChicagoUSA
  5. 5.Department of PhysicsCornell UniversityIthacaUSA

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