Conformal soft modes at elastic instabilities
Abstract
In case a crystal is close to a continuous elastic phase transition, pronounced critical fluctuations emerge. We show that on the level of linear elasticity theory the displacement vector for these critical modes obeys a condition reminiscent of the conformal Killing equation. For an isostructural instability, four critical modes arise corresponding to one dilation and three special conformal transformations. At crystal symmetry-breaking instabilities, the critical fluctuations include a continuum of modes even for crystals with finite size. For certain cases, these comprise the conformal transformations associated with two-dimensional Minkowski space. These results have implications for critical elastic phenomena as well as for extremal mechanical metamaterials.
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BibTeX
@misc{franke2026conformal,
title = {{Conformal soft modes at elastic instabilities}},
author = {Lars Franke and Nick Sander and Markus Garst},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17920},
eprint = {2610.17920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17920},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Conformal soft modes at elastic instabilities
AU - Lars Franke
AU - Nick Sander
AU - Markus Garst
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17920
UR - https://arxiv.org/abs/2610.17920
AB - In case a crystal is close to a continuous elastic phase transition, pronounced critical fluctuations emerge. We show that on the level of linear elasticity theory the displacement vector for these critical modes obeys a condition reminiscent of the conformal Killing equation. For an isostructural instability, four critical modes arise corresponding to one dilation and three special conformal transformations. At crystal symmetry-breaking instabilities, the critical fluctuations include a continuum of modes even for crystals with finite size. For certain cases, these comprise the conformal transformations associated with two-dimensional Minkowski space. These results have implications for critical elastic phenomena as well as for extremal mechanical metamaterials.
ER -