Exactly solved dynamics for an infinite-range spin system. II. Antiferromagnetic interactions

In a previous paper [E. Milotti, Phys. Rev. E 63, 026116 (2001)]. I have shown how to derive both thermodynamical and dynamical properties of an infinite-range Ising spin system with binary ferromagnetic interactions from the master equation for magnetization obtained from a simple spin dynamics. The same method can be adapted to different spin interactions: here I discuss die case of anti ferromagnetic interactions. This model permits a study of the static properties of the antiferromagnetic lattice, and it displays very clearly the differences between the antiferromagnetic and the ferromagnetic case with long-range interactions. The dynamical behavior of the antiferromagnetic system is simpler, and the magnetization always relaxes exponentially.