Scaling functions for rigidity transitions in disordered systems near 2 dimensions

ORAL  · Invited

Abstract

Critical scaling is often observed near rigidity transitions in soft matter systems. We analyze the critical scaling predicted by an exactly solvable dynamical mean-field theory for an isotropic rigidity transition. We extract renormalization group flows from the exact solution and characterize logarithmic corrections in two dimensions. This allows us to analytically calculate universal scaling functions for all linear response properties in all dimensions for certain kinds of nearly floppy soft matter.

*S.J.T., I.C., and J.P.S. were supported by NSF DMR-2327094. D.B.L. was supported by FAPESP through Grants No. 2021/14285-3 and No. 2022/09615-7.

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Publication: S. J. Thornton, I. Cohen, J. P. Sethna, and D. B. Liarte, Universal scaling solution for a rigidity transition: Renormalization group flows near the upper critical dimension, Phys. Rev. E 111, 045508 (2025).

Presenters

  • Stephen Thornton

    • Cornell University
    • University of California, Los Angeles

Authors

  • Stephen Thornton

    • Cornell University
    • University of California, Los Angeles

  • Danilo B Liarte

    • ICTP-SAIFR South American Institute for Fundamental Research

  • Itai Cohen

    • Cornell University

  • James Patarasp Sethna

    • Cornell University