Behavior of the overlap distribution of various spin glasses at low temperature

Numerical results for the probability distribution, $P(q,T)$, of the spin-overlap $q$ as a function of temperature $T$, is reported for several randomly frustrated systems. These include (i) random bond Ising systems, such as the Edwards-Andreson spin-glass model, (ii) site diluted systems which are geometrically frustrated, such as FCC lattices with $40\%$ of their sites occupied with up-down spins, and (iii) random-field systems. $P(q,T)$ stands for an average of $P_{\cal J}(q,T)$ over many system samples with different realizations of quenched randomness ${\cal J}$. We also report statistical fluctuations of $P_{\cal J}(q,T)$ which are relevant to the issue of self-averaging.