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  • Open Access

Reentrant Rigidity Transition in Planar Epithelia with Volume and Area Elasticity

Tanmoy Sarkar1,2 and Matej Krajnc1,*

  • *Contact author: matej.krajnc@ijs.si
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Phys. Rev. Lett. 136, 068404 – Published 12 February, 2026

DOI: https://doi.org/10.1103/ky2j-5nwx

Abstract

We find a reentrant columnar-to-squamous rigidity transition in three-dimensional (3D) epithelia, governed by volume and area elasticity. Our model maps to the classic 2D area- and perimeter-elasticity model but, unlike its 2D counterpart, shows compression-induced softening or stiffening, depending on the initial state. The phase diagram reveals floppy states with vanishing shear and in-plane bulk moduli, alongside a lateral-tension-driven discontinuous columnar-to-squamous transition. The critical behavior underlying the emergence of the reentrant transition belongs to the mean-field universality class.

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Phys. Rev. Lett. 136, 068404– Published 12 February, 2026
  • Received 20 May 2025
  • Accepted 22 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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