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arXiv · 2606.04614

Curvature-Controlled Infrared Regularization of Crystalline Membranes

Pablo A. Morales·Pavel Castro-Villarreal
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Abstract

We show that negative Gaussian curvature regularizes the infrared sector of crystalline membranes. In a covariant formulation of embedded elasticity, the Green strain contains a symmetry-required linear coupling between the normal phonon field and extrinsic curvature. Integrating out the in-plane phonons converts this coupling into a finite quadratic contribution to the inverse flexural response. Anomalous roughening is thereby replaced by curvature-controlled saturation, and the mechanism survives on minimal hyperbolic patches. Hyperbolic geometry preempts anomalous elasticity before the flat infrared regime is reached, implying the absence of a crumpling phase at the harmonic level. The same Gaussian-order coupling admits sound propagation in the infrared.

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Pablo A. Morales, Pavel Castro-Villarreal. 2026-06-03. Curvature-Controlled Infrared Regularization of Crystalline Membranes. https://arxiv.org/abs/2606.04614

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