Energy Scale Deformation on Regular Polyhedra

A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The induced by perturbations to uniform Hamiltonian, whose coefficients are determined bond coordinates. On tetrahedral, octahedral, and cubic clusters, perturbative terms do not affect ground state Hamiltonian when they sufficiently small. other hand, icosahedral dodecahedral it numerically confirmed that almost insensitive unless lead a discontinuous change in state. obtained results suggest existence generalization sine-square higher dimensions.