The critical behavior of a quenched random hypercubic sample of linear size L is considered, within the “random-$T_c$” field-theoretical model, by using the renormalization group method. A finite-size scaling behavior is established and analyzed near the upper critical dimension $d=4\mathrm{}-\epsilon$ and some universal results are obtained. The problem of self-averaging is clarified for different critical regimes.

• Received 11 July 2001

DOI:https://doi.org/10.1103/PhysRevE.65.026129