The frustrated Ising model (see e.g. this answer) is an example of a system that shows no unique ground state and many metastable states (its "energy landscape" is extremely complex). Frustration comes from the fact that the product of the coupling constants around a "plaquette" of the graph is negative (see e.g. the Wiki article "geometrical frustration").
This is quite clear, but I was wondering if there are continuous systems (as opposed to the Ising paradigm, that is a model on a graph) showing frustration. Are you aware of any examples that can be found in the statistical field theory literature?
An example, just to be concrete: we may imagine a model for a mixture of two substances, where the two densities fields (treated as scalar fields $\phi_1$ and $\phi_2$ in the spatial continuum with local interactions of the kind $\phi_1^a \phi_2^b$ for $a,b>0$) interact in such a way that they naturally tend to cluster and separate into blobs, similarly to what happens in the Cahn–Hilliard model for a binary fluid. Is there a notion of frustration for such "simple" two-field theories? How to define this notion (if any)?
