Spin glasses in a field: Three and four dimensions as seen from one space dimension

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, using both a new approach proposed recently, 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. © 2013 American Physical Society.

Spin glasses in a field: Three and four dimensions as seen from one space dimension Academic Article