I was trying to understand why for every spin configuration of a ferromagnetic system, there exists a corresponding isoenergetic state of an antiferromagnetic system. Can I treat an antiferromagnetically coupled 1-D ising model as a combination of two interpenetrating sublattices which are ferromagnetically coupled. If so, then how do I visualise this in 2 and 3 dimensions and extend the argument to d-dimensions? Basnically, how are these two systems (ferromagetically and antiferromagnetically correlated) thermodynamically equivalent? P.S: obviously, in the absence of a magnetic field.