Competing order in the mixed state of high-temperature superconductors

We examine the low-temperature behavior of the mixed state of a layered superconductor in the vicinity of a quantum critical point separating a pure superconducting phase from a phase in which a competing order coexists with superconductivity. At zero temperature, we find that there is an avoided critical point in the sense that the phase boundary in the limit B-->0 does not connect to the B=0 critical point. Consequently, there exists a quasi-one-dimensional (1D) regime of the phase diagram, in which the competing order is largely confined to 1D "halos" about each vortex core, and in which interactions between neighboring vortices, although relevant at low temperature, are relatively weak.