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

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$d_c=d-2$\mathrm{.}Thus,thevalue$-1/3$ predicted in previous literature holds only in the limit $d_c\to \mathrm{\infty }$.