We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters A and G show that the order parameter is not self-averaging, consistent with a zero-temperature thermal exponent value ${\theta }^{\prime }\simeq 0,$ and confirms the validity of the relation $G=1/3\mathrm{}$ in the thermodynamic limit in the whole low-temperature phase, as predicted by stochastic stability arguments.

• Received 22 August 2003

DOI:https://doi.org/10.1103/PhysRevB.68.224430