in panel (c) we present the FSS of the maxima of the average magnetic susceptibility [ χ ] ∗ av (filled squares) and also the average of the individual maxima [ χ ∗ ]$_{av}$ (open triangles). The solid and dotted lines present linear fit- tings using the total lattice range spectrum, giving the estimates 1 . 751(5) and 1 . 756(9) for the ratio γ/ν in very good agreement with the expected value 1 . 75 of the pure system. For the average [ χ ] ∗ av the error bars indicate the statistical errors due to the finite number of the realiza- tions, as discussed in Sec. I. For the average [ χ ∗ ]$_{av}$ the errors bars shown reflect now the relatively large sample- to-sample fluctuations. Finally, using the latter sample-to-sample fluctuations, we construct the ratio R$_{[}$$_{χ}$ ∗ ] av and plot it as a function of the inverse linear size, as shown in the inset of Fig. 8(c). Clearly, for the present model the limiting value of R$_{[}$$_{χ}$ ∗ ] av is non-zero, indicating, as expected also for marginal dis- ordered systems [74], a strong violation of self-averaging. The effects induced by the presence of quenched bond randomness on the critical behavior of the 2d Ising spin model embedded in the triangular lattice have been in- vestigated by an efficient entropic scheme based on the Wang-Landau algorithm. In the first part of our study we presented the finite-size scaling behavior of the pure model, for which we calculated with high accuracy the critical exponents and the coefficients of the specific heat’s logarithmic expansion at the critical point. Our results are in full agreement with the exact expansion The authors would like to thank Ralph Kenna and Walter Selke for their useful comments and a critical reading of the manuscript. In the second part of our study we investigated the critical properties of the disordered system. The pre- sented detailed finite-size scaling analysis along the lines of the two existing scenarios - strong versus weak univer- sality - strongly supports the scenario of strong universal- ity. Thus, our results are in agreement with the behavior predicted originally on theoretical basis many years ago by Dotsenko and Dotsenko [17], Jug [18], Shalaev [19], Shankar [20], and Ludwig [21] and verified by simula- tions in recent years for the square random Ising model by several authors [39–41, 43, 44, 48, 58, 59]. Particular interest was paid to the sample-to-sample fluctuations of the random model and their scaling behavior that were used as a successful alternative approach to estimate the critical temperature and the correlation length’s expo- nent. Closing, we would like to note that another inter- esting candidate, that has not been studied before in the triangular lattice, is the 3-state Potts model, which, in its pure version, has a positive specific-heat exponent. 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