Schramm-Loewner evolution in 2d rigidity percolation
arXiv:2301.07614 · doi:10.1103/PhysRevLett.132.018201
Abstract
Amorphous solids may resist external deformation such as shear or compression while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter we exploit this finding to characterise the universality class of central-force rigidity percolation (RP), using Schramm-Loewner Evolution (SLE) theory. We provide numerical evidences that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant , we obtain the estimation for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension and correlation length exponent , providing new, non-trivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.
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