Bounds on the static electric susceptibility of nonequilibrium cubic crystals: A study of sample shape dependence

Contrary to the conventional view that static electric susceptibility χ ( 0 ) must always be positive, materials not in thermodynamic equilibrium may exhibit χ ( 0 ) < 0 . Preliminary experimental evidence within active metamaterials supported this possibility, though full validation remained open. A theoretical framework had been developed using two approaches: the finite crystal method (FCM) and the infinite crystal method (ICM). For cubic arrays of entities with negative static polarizability, the ICM showed shape-dependent behavior, yielding accurate bounds only when the summation order corresponded to slab-like geometries. This raised the question of whether the FCM is similarly sensitive to the overall sample shape. Here, we test the FCM across four distinct, well-established sample shapes: rhombohedron, ‘parallelepiped slab’, ‘parallelepiped needle’, and sphere, for each of the cubic crystal structure. We show that, unlike the ICM, the FCM produces convergent and shape-independent bounds on critical polarizability and χ ( 0 ) , establishing it as a rigorous method for nonequilibrium cubic crystals. • Shows that FCM gives shape-independent bounds on static susceptibility unlike ICM. • Compares rhombohedron, slab, needle, and sphere across SC, BCC, and FCC lattices. • Finds spheres and rhombohedra most accurate shapes in FCM, with ≤ 0 . 6 % uncertainty. • Provides a rigorous framework for testing negative static susceptibility feasibility.