Varda F. Hagh, Robert Dennis, Eric Corwin

Periodic boundary conditions are used in studies of physical systems to lessen finite-size effects. However, the use of these boundaries can lead to strange and unintuitive results. For instance, spring networks or critically jammed sphere packings that are rigid with a few states of self-stress can become floppy through the creation of new zero modes when they are replicated periodically. Our observations show that this is only true in systems with fewer than the dimension, d, states of self-stress. To understand the reason behind the emergence of new zero modes, we draw links between this result and the constraints needed for shear stability, as well as the Guest-Hutchinson modes found in crystals.