The de Almeida–Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature $T$ and magnetic field $h$ plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that, when the dimension $d$ of space is just above six, there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime, where the RG flows run away to infinite coupling strength; as $d$ approaches six from above, the MCP approaches the zero-field critical point exponentially in $1/(d-6)$. Thus, on the AT line, perturbation theory for the critical properties breaks down at a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when $d\le 6$, as was known previously. We calculate the exponents at the MCP to first order in $ϵ=d-6>0$. The fate of the MCP as $d$ increases from just above six to infinity is not known.

• Received 28 January 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.130602