  The copper-oxide based high temperature superconductors have complex phase
diagrams with multiple ordered phases. It even appears that the highest
superconducting transition temperatures for certain cuprates are found in
samples which display simultaneous onset of magnetism and superconductivity. We
show here how the thermodynamics of fluid mixtures - a touchstone for chemists
as well as hard and soft condensed matter physics - accounts for this startling
observation, as well as many other properties of the cuprates in the vicinity
of the instability towards ``striped'' magnetism.
