  We study the existence of a line of transitions of an Ising spin glass in a
magnetic field-known as the de Almeida-Thouless line-using one-dimensional
power-law diluted Ising spin-glass models. We choose the power-law exponent to
have values that approximately correspond to three- and four-dimensional
nearest-neighbor systems and perform a detailed finite-size scaling analysis of
the data for large linear system sizes, both using a new approach proposed
recently [Phys. Rev. Lett. 103, 267201 (2009)], as well as traditional
approaches. Our results for the model corresponding to a three-dimensional
system are consistent with there being no de Almeida-Thouless line, although
the new finite-size scaling approach does not rule one out. For the model
corresponding to four space dimensions, the new and traditional finite-size
scaling analyses give conflicting results, indicating the need for a better
understanding of finite-size scaling of spin glasses in a magnetic field.
