Multiple reentrance and fractal phase boundaries in the Barker–Fock model

The Barker–Fock model, which addresses the issue of closed-loop phase diagrams in binary liquid mixtures, is shown to exhibit a wealth of interesting and rather unexpected physical phenomena. For example, renormalization-group studies indicate that in addition to the standard closed-loop diagrams seen in many binary liquid mixtures, the Barker–Fock model also yields multiple reentrance – perhaps of unlimited degree. In addition, one of the “phase boundaries” in the model is actually many separate phases mixed together to form a “fractal foam”. Behavior of this kind is interesting in its own right, and particularly so when the underlying model has direct physical relevance.