The system with exponentially degenerate vacuum state

I suggest and examine artificial material which has exponentially degenerate vacuum state. The corresponding Hamiltonian contains only exotic four-spin interaction term. Each vacuum state is realized as a particular spin configuration separated from others by potential barriers. The benefit of such system in practical applications is that it can be used as high density magnetic recording system which can reduce storage of one bit information to $nm$ scale. The information is stored as a particular vacuum state of the system. The process of recording can be visualized as a process in which the system moves from one vacuum state to another. Storing information in the form of different vacuum states separated by potential barriers will allow to protect it from fluctuations and for a longer time. These materials can be realized as lattices of nuclear spins with specially adjusted interactions. The planes of flipped spins can in principle be of atomic scale.