Differential Poisson's ratio of a crystalline two-dimensional membrane

TL;DR

This paper calculates the universal behavior of the differential Poisson's ratio for large-dimensional crystalline membranes, revealing it approaches -1/3 with corrections depending on the embedding space's dimensionality.

Contribution

It provides the first analytical derivation of the universal value and dimensional dependence of the differential Poisson's ratio in high-dimensional membranes.

Findings

The differential Poisson's ratio approaches -1/3 as dimensionality increases.

The ratio has a power-law correction depending on the embedding space's dimension.

Previous predictions of -1/3 are only valid in the infinite-dimensional limit.

Abstract

We compute the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d \gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $\nu = -1/3 + 0.016/d_c + O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.