We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.
This is indeed a problem, encountered e.g. when you consider a system with dipoles. There exist methods to split off the long range part of the fields, namely Ewald summation.