Phase transition in a ferromagnetic fluid

The correlation inequalities of Fortuin, Kasteleyn, and Ginibre (FKG) are used in conjunction with those of Griffiths, Kelly, and Sherman (GKS) to demonstrate the existence of a ferromagnetic phase transition in a continuum fluid of classical particles carrying Ising-like spins and having suitable magnetic and non-magnetic interactions. The procedure involves finding a lower bound on the magnetization of the fluid in terms of that of a suitable spin system on a lattice.