Quantum Critical Regime

I'll post some work related stuff too, so dear reader wouldn't get confused about why I am here at ETH. Let's consider a 1dimensional chain of 1/2 spins with alternating antiferromagnetic Heisenberg exchange coupling constants denoted by Ja and Jb. If Ja is much larger than Jb then the ground state of such system will be singlets on dimers on bonds "a" and for vice versa parameter values Jb >> Ja there will be dimers on bonds "b". When Jb=Ja then we get a ground state described by Luttinger Liquid (in 3D we would get a nice Neel order, but not in 1D). Somewhere between these regions lies a quantum critical point at which ground state jumps form one order to another. With temperature above zero (Kelvins of course) this point gets wider in phase diagram and becomes quantum critical regime (QCR). Now the question is: what order such spin system has in QCR and by which easily measurable observables should one try to detect such state? I am no theorist, so will search the literature and you'll get the answer when I do. If ya know the answer just write it in the comments :)