# Periodic ground state 1-dim ising model

Good evening! I'm at the beginning of my study about the Ising model and it has been proposed to me this problem: Find all periodic ground-state configuration for the following one-dimensional Ising model of interacting spins, $s_i=+1$ or $-1$ $$H=-\sum_{i\in\mathbb{Z}} (s_{i}s_{i+1}-s_{i}s_{i+2}-4s_{i}s_{i+3})$$ Actually, I don't know how to procede. I know that the ground states, by definition, are the configuration of minimal energy. But then, is this possible to compute these configuration for this specific model in an explicit way? I hope that someone could give me a hint, because I think that I'm a little bit confused.. Thank you very much!