Almeida Thouless Line in Vector Spin Glasses

The de Almeida Thouless line in the magnetic field-temperature plane of spin glasses, separates a high-temperature, high-field paramagnetic phase from a spin glass phase. It is a characteristic feature of Ising spin glasses in the mean field (infinite-range) limit. Here we show that an AT line also occurs for infinite-range \textit{vector} spin glasses in a \textit{random} magnetic field, which does not appear to have been appreciated before. We verify this conclusion by numerical simulations.