Free energy of spin glasses with multiple types.

In the standard SK spin glass, the energy function involves interaction 
terms between all pairs of spins. A bipartite version of this model can 
be obtained by splitting the spins into two groups, which we can 
visualize as forming two layers, and by keeping only interaction terms 
that go from one to the other layer. For this and other models that 
incorporate a finite number of types of spins, the asymptotic behavior 
of the free energy remains mathematically mysterious. I will present the 
difficulties arising there, and some partial progress.