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

Abstract 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 d c , with a power-law expansion ν = − 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 → ∞ .