  I summarize recent results, obtained with E. Demler, K. Park, A. Polkovnikov,
M. Vojta, and Y. Zhang, on spin and charge correlations near a magnetic quantum
phase transition in the cuprates. STM experiments on slightly overdoped BSCCO
(J.E. Hoffman et al., Science 295, 466 (2002)) are consistent with the
nucleation of static charge order coexisting with dynamic spin correlations
around vortices, and neutron scattering experiments have measured the magnetic
field dependence of static spin order in the underdoped regime in LSCO (B. Lake
et al., Nature 415, 299 (2002)) and LaCuO_4+y (B. Khaykovich et al., Phys. Rev.
B 66, 014528 (2002)). Our predictions provide a semi-quantitative description
of these observations, with only a single parameter measuring distance from the
quantum critical point changing with doping level. These results suggest that a
common theory of competing spin, charge and superconducting orders provides a
unified description of all the cuprates.
