STRANGE ATTRACTORS IN AN ANTIFERROMAGNETIC ISING-MODEL

The three-site antiferromagnetic Ising model on Husimi tree is investi gated in an external magnetic field. The full bifurcation diagram, inc luding chaos, of the magnetization is exhibited. With the ''thermodyna mic formalism'', we investigate the antiferromagnetic Ising model in t he case of fully developed chaos and describe the chaotic properties o f this statistical mechanical system via the invariants characterizing a strange attractor. It is shown that this system displays in the cha otic region a phase transition at a positive ''temperature'' whereas i n a class of maps close to x --> 4x(1-x), the phase transitions occur at negative ''temperatures''. The Frobenius-Perron recursion equation is numerically solved and the density of the invariant measure is obta ined.