Spin-density-wave order in cuprates

We study the nature of the two-dimensional quantum critical point separating two phases with and without long-range spin-density-wave order, which has been recently observed in cuprate superconductors. We consider the Landau-Ginzburg-Wilson Hamiltonian associated with the spin-density critical modes, perform a mean-field analysis of the phase diagram, and study the corresponding renormalization-group flow in two different perturbative schemes at five and six loops, respectively. The analysis supports the existence of a stable fixed point in the full theory whose basin of attraction includes systems with collinear spin-density-wave order, as observed in experiments. The stable fixed point is characterized by an enlarged O(4)circle times O(3) symmetry. The continuous transition observed in experiments is expected to belong to this universality class. The corresponding critical exponents are nu=0.9(2) and eta=0.15(10).