Nonlinear and spin-glass susceptibilities of three site-diluted systems

The nonlinear magnetic $\chi_{3}$ and spin-glass $\chi_{sg}$ susceptibilities in zero applied field are obtained, from tempered Monte Carlo simulations, for three different spin glasses (SGs) of Ising spins with quenched site disorder. We find that the relation $-T^3\chi_3=\chi_{sg}-2/3$ ($T$ is the temperature), which holds for Edwards-Anderson SGs, is approximately fulfilled in canonical-like SGs. For nearest neighbor antiferromagnetic interactions, on a 0.4 fraction of all sites in fcc lattices, as well as for spatially disordered Ising dipolar (DID) systems, $-T^3\chi_3$ and $\chi_{sg}$ appear to diverge in the same manner at the critical temperature $T_{sg}$. However, $-T^3\chi_3$ is smaller than $\chi_{sg}$ by over two orders of magnitude in the diluted fcc system. In DID systems, $-T^3\chi_3/\chi_{sg}$ is very sensitive to the systems aspect ratio. Whereas near $T_{sg}$, $\chi_{sg}$ varies by approximately a factor of 2 as system shape varies from cubic to long-thin-needle shapes, $\chi_3$ sweeps over some four decades.