# Strong interacting v.s. Strong Coupling v.s. Strong Correlated

One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters.

It seems to me that some physicists in the fields often mix the usages of these twos: Strong Coupling, Strong Correlated.

However, in my viewpoint, they are NOT the exactly same, I regard that

$\bullet$ Strong Coupling: implies the large coupling of interactions comparing to the free part of theory. Say, suppose there is a Lagrangian description, then the action $S$ $$S=S_{free} +g S_{interact}$$ the Strong Coupling means $g >>1$. So this can be the confined phases of QCD, where coupling $g$ of quarks and gluons runs large.

--

$\bullet$ Strong Correlated: in my view, usually implies the fractionalization of the elementary particles into fractional quantum numbers. For example, this happens at 1+1D Luttinger liquids, where spin and charge can separated their degree of freedom from the elementary constituents(electrons), but the system needs NOT to be Strong Coupling. i.e. this example is Strong Correlated but NOT Strong Coupling. This is about the fields of Strong Correlated Electron on arXiv.

--

My question, so what are other examples of systems that are:

1. YES Strong Coupling and YES Strong Correlated

2. YES Strong Coupling but NOT Strong Correlated

3. NOT Strong Coupling but YES Strong Correlated

• And what about the difference between coupling and interaction? it follows from your post that there's one but you don't comment about it, could you clarify it, please? Also, what it means the $S_{free}$? it includes the kinetic part? – cla Jan 5 '17 at 16:01