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≫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 dc, with a power-law expansion ν=−1∕3+0.016∕dc+O(1∕dc2), where dc=d−2. Thus, the value −1∕3 predicted in previous literature holds only in the limit dc→∞.