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  • Open Access

Self-avoiding tethered surfaces are always flat

A. D. Chen1, M. C. Gandikota2, M. J. Kim1, and A. Cacciuto1,*

  • *Contact author: ac2822@columbia.edu
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Phys. Rev. Research 8, 023015 – Published 2 April, 2026

DOI: https://doi.org/10.1103/28pb-jly6

Abstract

The scaling behavior of fully flexible elastic tethered surfaces has been debated for decades. Some theories predict that self-avoiding surfaces would crumple in the absence of bending rigidity, while most simulations suggested that they would remain flat. Recent simulations on ideal membranes with lattice perforations suggest that systematically removing surface area from a membrane may provide an alternative way to crumpling self-avoiding surfaces. We perform extensive numerical simulations of two models of fully flexible elastic tethered surfaces in which self-avoidance can be systematically and continuously tuned to the ideal limit. We show that in the thermodynamic limit, these surfaces remain flat with a size exponent ν=1 for any finite degree of self-avoidance, with or without membrane perforations.

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Phys. Rev. Research 8, 023015– Published 2 April, 2026
  • Received 30 September 2025
  • Accepted 24 February 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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