Self-averaging of singular thermodynamic quantities at criticality for randomly and thermally diluted three-dimensional Ising systems has been studied by the Monte Carlo approach. Substantially improved self-averaging is obtained for critically clustered (critically thermally diluted) vacancy distributions in comparison with the observed self-averaging for purely random diluted distributions. Critically thermal dilution, leading to maximum relative self-averaging, corresponds to the case when the characteristic vacancy ordering temperature (θ) is made equal to the magnetic critical temperature for the pure three-dimensional (3D) Ising systems ${(T}_c^{3\mathrm{D}}).\mathrm{}$ For the case of a high ordering temperature $\left(\theta \gg T_c^{3\mathrm{D}}\right),$ the self-averaging obtained is comparable to that in a randomly diluted system.

• Received 20 January 1999

DOI:https://doi.org/10.1103/PhysRevE.60.2394