Ising models with several phase transitions

We give a physical explanation for the existence of multiple phase transitions in certain Ising-like models. They are due to the presence of competing interactions propagating along paths of different lengths. The idea is illustrated by constructing Ising models with an arbitrary number of phase transitions. The physical insight thus gained is used to develop a mean-field approximation which reproduces correctly the phase diagram of the two-dimensional fcc Ising problem. The mean-field approach can be generalized to three dimensions.