I will discuss results of recent numerical bootstrap work performed for systems with cubic symmetry. Under certain assumptions, we find an isolated region in parameter space, which given prior intuition with the numerical bootstrap, indicates the existence of a CFT in this region. We find critical exponents for the conjectured CFT which are in discrepancy with the epsilon expansion (but in good agreement with experiments for structural phase transitions). The disagreement of critical exponents for structural phase transitions calculated in the epsilon expansion with those measured in experiments is something that was noticed since the 70s. I will briefly discuss some resolutions proposed at the time.